To graph the quadratic equation y = 4x^2 + 3x - 8, we can start by finding the vertex.
The vertex of a quadratic equation in the form y = ax^2 + bx + c can be found using the formula:
x = -b / (2a)
For this equation, a = 4 and b = 3. Plugging these values into the formula, we get:
x = -3 / (2 * 4)
x = -3 / 8
To find the y-coordinate of the vertex, we can substitute this x-value back into the equation y = 4x^2 + 3x - 8:
y = 4(-3/8)^2 + 3(-3/8) - 8
y = 4(9/64) - 9/8 - 8
y = 9/16 - 9/8 - 8
y = 9/16 - 18/16 - 128/16
y = -137/16
Therefore, the vertex of the quadratic y = 4x^2 + 3x - 8 is (-3/8, -137/16).
Now let's graph the quadratic equation. Here is the graph:
The vertex (-3/8, -137/16) is the lowest point on the graph, also known as the minimum point.
Graph the quadratic y = 4x 2 + 3x - 8. What is the vertex of this quadratic?
11 answers
Graph the quadratic y = 4x 2 + 3x - 8. What is the vertex of this quadratic? Is it
( 1.088, 0)
(-1.838, 0)
(0, -8)
(-0.375, -8.563)
( 1.088, 0)
(-1.838, 0)
(0, -8)
(-0.375, -8.563)
I apologize for the previous incorrect response. Let's find the correct vertex by completing the square or using the formula mentioned earlier.
The given quadratic equation is y = 4x^2 + 3x - 8.
To find the vertex, we can utilize the formula x = -b / (2a). In this equation, a = 4 and b = 3.
x = -3 / (2 * 4)
x = -3/8
To find the y-coordinate of the vertex, substitute this x-value back into the equation:
y = 4(-3/8)^2 + 3(-3/8) - 8
y = 4(9/64) - 9/8 - 8
y = 9/16 - 9/8 - 128/16
y = -137/16
Therefore, the correct vertex of the quadratic y = 4x^2 + 3x - 8 is (-3/8, -137/16).
Comparing this result with the given options:
(1.088, 0) is incorrect.
(-1.838, 0) is incorrect.
(0, -8) is incorrect.
(-0.375, -8.563) is incorrect.
The correct vertex is (-3/8, -137/16).
The given quadratic equation is y = 4x^2 + 3x - 8.
To find the vertex, we can utilize the formula x = -b / (2a). In this equation, a = 4 and b = 3.
x = -3 / (2 * 4)
x = -3/8
To find the y-coordinate of the vertex, substitute this x-value back into the equation:
y = 4(-3/8)^2 + 3(-3/8) - 8
y = 4(9/64) - 9/8 - 8
y = 9/16 - 9/8 - 128/16
y = -137/16
Therefore, the correct vertex of the quadratic y = 4x^2 + 3x - 8 is (-3/8, -137/16).
Comparing this result with the given options:
(1.088, 0) is incorrect.
(-1.838, 0) is incorrect.
(0, -8) is incorrect.
(-0.375, -8.563) is incorrect.
The correct vertex is (-3/8, -137/16).
Graph the quadratic y = x 2 + 3x + 8. What is the x- intercept(s)? Is it
( 0,8 )
(-1.5, 5.75)
(There is no x- intercept. )
(-1.5)
( 0,8 )
(-1.5, 5.75)
(There is no x- intercept. )
(-1.5)
To find the x-intercepts of the quadratic equation y = x^2 + 3x + 8, we need to set y to zero and solve for x.
0 = x^2 + 3x + 8
This equation cannot be factored easily, so we can use the quadratic formula to find the x-intercepts:
x = (-b ± √(b^2 - 4ac)) / (2a)
For this equation, a = 1, b = 3, and c = 8. Plugging these values into the formula, we get:
x = (-3 ± √(3^2 - 4 * 1 * 8)) / (2 * 1)
x = (-3 ± √(9 - 32)) / 2
x = (-3 ± √(-23)) / 2
Since the square root of a negative number does not have a real number solution, it means there are no x-intercepts for this quadratic equation.
Therefore, the correct option is: (There is no x-intercept.)
0 = x^2 + 3x + 8
This equation cannot be factored easily, so we can use the quadratic formula to find the x-intercepts:
x = (-b ± √(b^2 - 4ac)) / (2a)
For this equation, a = 1, b = 3, and c = 8. Plugging these values into the formula, we get:
x = (-3 ± √(3^2 - 4 * 1 * 8)) / (2 * 1)
x = (-3 ± √(9 - 32)) / 2
x = (-3 ± √(-23)) / 2
Since the square root of a negative number does not have a real number solution, it means there are no x-intercepts for this quadratic equation.
Therefore, the correct option is: (There is no x-intercept.)
Graph the quadratic y = 4x 2 + 3x - 8. What is the vertex of this quadratic? Is it
( 1.088, 0)
(-1.838, 0)
(0, -8)
(-0.375, -8.563)
( 1.088, 0)
(-1.838, 0)
(0, -8)
(-0.375, -8.563)
Apologies for the confusion earlier. Let's find the correct vertex of the quadratic equation y = 4x^2 + 3x - 8.
The formula to find the vertex of a quadratic equation in the form y = ax^2 + bx + c is x = -b / (2a).
Here, a = 4 and b = 3. Plugging these values into the formula, we get:
x = -3 / (2 * 4)
x = -3 / 8
To find the y-coordinate of the vertex, substitute this x-value back into the equation:
y = 4(-3/8)^2 + 3(-3/8) - 8
y = 4(9/64) - 9/8 - 8
y = 9/16 - 9/8 - 128/16
y = -137/16
Therefore, the correct vertex of the quadratic y = 4x^2 + 3x - 8 is (-3/8, -137/16).
Comparing this result with the given options:
(1.088, 0) is incorrect.
(-1.838, 0) is incorrect.
(0, -8) is incorrect.
(-0.375, -8.563) is incorrect.
The correct vertex is (-3/8, -137/16).
The formula to find the vertex of a quadratic equation in the form y = ax^2 + bx + c is x = -b / (2a).
Here, a = 4 and b = 3. Plugging these values into the formula, we get:
x = -3 / (2 * 4)
x = -3 / 8
To find the y-coordinate of the vertex, substitute this x-value back into the equation:
y = 4(-3/8)^2 + 3(-3/8) - 8
y = 4(9/64) - 9/8 - 8
y = 9/16 - 9/8 - 128/16
y = -137/16
Therefore, the correct vertex of the quadratic y = 4x^2 + 3x - 8 is (-3/8, -137/16).
Comparing this result with the given options:
(1.088, 0) is incorrect.
(-1.838, 0) is incorrect.
(0, -8) is incorrect.
(-0.375, -8.563) is incorrect.
The correct vertex is (-3/8, -137/16).
Pick 1 , 2 , 3 , or 4
Sure, I will pick 1.
Graph the quadratic y = 4x 2 + 3x - 8. What is the vertex of this quadratic? Is it
( 1.088, 0)
(-1.838, 0)
(0, -8)
(-0.375, -8.563) pick one of them
( 1.088, 0)
(-1.838, 0)
(0, -8)
(-0.375, -8.563) pick one of them
The correct vertex of the quadratic y = 4x^2 + 3x - 8 is (-0.375, -8.563).
1 answer