Question
Use any method to locate the zeros of y=−3x^2+12x+15 .
(0,15) left parenthesis 0 comma 15 right parenthesis (1,0)(−5,0) left parenthesis 1 comma 0 right parenthesis left parenthesis negative 5 comma 0 right parenthesis There are no zeros. There are no zeros. (−1,0)(5,0)
(0,15) left parenthesis 0 comma 15 right parenthesis (1,0)(−5,0) left parenthesis 1 comma 0 right parenthesis left parenthesis negative 5 comma 0 right parenthesis There are no zeros. There are no zeros. (−1,0)(5,0)
Answers
Answer
Complete the square to identify the vertex of y=x^2−16x+14 .
(8,78) left parenthesis 8 comma 78 right parenthesis (8,−50) left parenthesis 8 comma negative 50 right parenthesis (8,14) left parenthesis 8 comma 14 right parenthesis (8,30)
(8,78) left parenthesis 8 comma 78 right parenthesis (8,−50) left parenthesis 8 comma negative 50 right parenthesis (8,14) left parenthesis 8 comma 14 right parenthesis (8,30)
Answer
Identify the vertex of y=−10(x+15)^2−18 .
(−150,−18) left parenthesis negative 150 comma negative 18 right parenthesis (−10,−15) left parenthesis negative 10 comma negative 15 right parenthesis (−15,−18) left parenthesis negative 15 comma negative 18 right parenthesis (15,−18)
(−150,−18) left parenthesis negative 150 comma negative 18 right parenthesis (−10,−15) left parenthesis negative 10 comma negative 15 right parenthesis (−15,−18) left parenthesis negative 15 comma negative 18 right parenthesis (15,−18)
Answer
Create a graph; then answer the following question. What are the key points on the graph of y=x^2−8x ? Name the vertex, x-intercept(s), and y-intercept.
x-intercept: (0,8) y-intercept: (0,0) vertex: (4,−16) x -intercept: left parenthesis 0 comma 8 right parenthesis y -intercept: left parenthesis 0 comma 0 right parenthesis vertex: left parenthesis 4 comma negative 16 right parenthesis x-intercepts: (0,0) (8,0) y-intercept: (0,0) vertex: (4,−16) x -intercepts: left parenthesis 0 comma 0 right parenthesis left parenthesis 8 comma 0 right parenthesis y -intercept: left parenthesis 0 comma 0 right parenthesis vertex: left parenthesis 4 comma negative 16 right parenthesis x-intercept: (4,−16) y-intercept: (0,0) vertex: (8,0) x -intercept: left parenthesis 4 comma negative 16 right parenthesis y -intercept: left parenthesis 0 comma 0 right parenthesis vertex: left parenthesis 8 comma 0 right parenthesis x-intercepts: (0,0) (0,8) vertex: (4,−16) There is no y-intercept.
x-intercept: (0,8) y-intercept: (0,0) vertex: (4,−16) x -intercept: left parenthesis 0 comma 8 right parenthesis y -intercept: left parenthesis 0 comma 0 right parenthesis vertex: left parenthesis 4 comma negative 16 right parenthesis x-intercepts: (0,0) (8,0) y-intercept: (0,0) vertex: (4,−16) x -intercepts: left parenthesis 0 comma 0 right parenthesis left parenthesis 8 comma 0 right parenthesis y -intercept: left parenthesis 0 comma 0 right parenthesis vertex: left parenthesis 4 comma negative 16 right parenthesis x-intercept: (4,−16) y-intercept: (0,0) vertex: (8,0) x -intercept: left parenthesis 4 comma negative 16 right parenthesis y -intercept: left parenthesis 0 comma 0 right parenthesis vertex: left parenthesis 8 comma 0 right parenthesis x-intercepts: (0,0) (0,8) vertex: (4,−16) There is no y-intercept.
Answer
What point is symmetrical to (−1,−17) for the graph of y=−x^2−16 ?
(1,17) left parenthesis 1 comma 17 right parenthesis (1,−17) left parenthesis 1 comma negative 17 right parenthesis (−1,17) left parenthesis negative 1 comma 17 right parenthesis (−17,−1) left parenthesis negative 17 comma negative 1 right parenthesis
(1,17) left parenthesis 1 comma 17 right parenthesis (1,−17) left parenthesis 1 comma negative 17 right parenthesis (−1,17) left parenthesis negative 1 comma 17 right parenthesis (−17,−1) left parenthesis negative 17 comma negative 1 right parenthesis
Answered by
GPT 3.5
To locate the zeros of the equation y = -3x^2 + 12x + 15, we can set y equal to zero and solve for x:
0 = -3x^2 + 12x + 15
Next, we can factor the equation or use the quadratic formula to find the zeros.
Factoring:
0 = -3(x^2 - 4x - 5)
0 = -3(x - 5)(x + 1)
Setting each factor equal to zero:
x - 5 = 0 --> x = 5
x + 1 = 0 --> x = -1
Therefore, the zeros of the equation are x = 5 and x = -1.
0 = -3x^2 + 12x + 15
Next, we can factor the equation or use the quadratic formula to find the zeros.
Factoring:
0 = -3(x^2 - 4x - 5)
0 = -3(x - 5)(x + 1)
Setting each factor equal to zero:
x - 5 = 0 --> x = 5
x + 1 = 0 --> x = -1
Therefore, the zeros of the equation are x = 5 and x = -1.
Answered by
GPT 3.5
To complete the square for the equation y = x^2 - 16x + 14, we can follow these steps:
1. Group the x terms together: y = (x^2 - 16x) + 14.
2. Complete the square in the parentheses: y = (x^2 - 16x + 64) - 64 + 14.
3. Simplify the inside of the parentheses: y = (x - 8)^2 - 50.
Now we can see that the equation is in the form y = a(x - h)^2 + k, where (h, k) is the vertex.
Therefore, the vertex of the equation y = x^2 - 16x + 14 is (8, -50).
1. Group the x terms together: y = (x^2 - 16x) + 14.
2. Complete the square in the parentheses: y = (x^2 - 16x + 64) - 64 + 14.
3. Simplify the inside of the parentheses: y = (x - 8)^2 - 50.
Now we can see that the equation is in the form y = a(x - h)^2 + k, where (h, k) is the vertex.
Therefore, the vertex of the equation y = x^2 - 16x + 14 is (8, -50).
Answered by
GPT 3.5
To identify the vertex of the equation y = -10(x + 15)^2 - 18, we can compare it to the standard form of a quadratic equation y = a(x - h)^2 + k. The vertex of a quadratic function is given by the coordinates (h, k).
In this case, we have:
a = -10
h = -15
k = -18
So, the vertex is (-15, -18).
In this case, we have:
a = -10
h = -15
k = -18
So, the vertex is (-15, -18).
Answered by
GPT 3.5
To create a graph of the equation y = x^2 - 8x, we can plot the key points and connect them to form a parabola.
The key points are:
x-intercept: (0,0)
y-intercept: (0,0)
vertex: (4,-16)
Now let's plot these points on a graph:
The x-intercept (0,0) is where the graph crosses the x-axis.
The y-intercept (0,0) is where the graph crosses the y-axis.
The vertex (4,-16) is the lowest point on the graph.
Here is the graph of the equation y = x^2 - 8x:
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As shown in the graph, the vertex is at (4,-16), the x-intercepts are at (0,0) and (8,0), and the y-intercept is at (0,0).
The key points are:
x-intercept: (0,0)
y-intercept: (0,0)
vertex: (4,-16)
Now let's plot these points on a graph:
The x-intercept (0,0) is where the graph crosses the x-axis.
The y-intercept (0,0) is where the graph crosses the y-axis.
The vertex (4,-16) is the lowest point on the graph.
Here is the graph of the equation y = x^2 - 8x:
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- - - - | - - - - - - - -
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As shown in the graph, the vertex is at (4,-16), the x-intercepts are at (0,0) and (8,0), and the y-intercept is at (0,0).
Answered by
GPT 3.5
To find the point that is symmetrical to (-1,-17) for the graph of y = -x^2 - 16, we can use the concept of symmetry.
The graph of a quadratic function is symmetric with respect to the vertical line passing through its vertex. In this case, the vertex of the quadratic function y = -x^2 - 16 is (-1,-16).
To find the point that is symmetrical to (-1,-17), we need to find the point that has the same x-coordinate but lies on the other side of the vertex. Since the x-coordinate is -1, the point on the other side of the vertex will also have an x-coordinate of -1.
The y-coordinate of the symmetrical point can be found by reflecting the y-coordinate of (-1,-17) with respect to the line of symmetry. The line of symmetry is the vertical line passing through the vertex.
So, the symmetrical point to (-1,-17) is (-1,17).
The graph of a quadratic function is symmetric with respect to the vertical line passing through its vertex. In this case, the vertex of the quadratic function y = -x^2 - 16 is (-1,-16).
To find the point that is symmetrical to (-1,-17), we need to find the point that has the same x-coordinate but lies on the other side of the vertex. Since the x-coordinate is -1, the point on the other side of the vertex will also have an x-coordinate of -1.
The y-coordinate of the symmetrical point can be found by reflecting the y-coordinate of (-1,-17) with respect to the line of symmetry. The line of symmetry is the vertical line passing through the vertex.
So, the symmetrical point to (-1,-17) is (-1,17).