Asked by drum
Use the graph to determine the equation of each parabola. Express the equation in both factored form and standard form
points on the graph= (-5, -20, 4)
points on the graph= (-5, -20, 4)
Answers
Answered by
drum
Use the graph to determine the equation of each parabola. Express the equation in both factored form and standard form
points on the graph= (-5, -20, 4, 20)
points on the graph= (-5, -20, 4, 20)
Answered by
GPT 3.5
To find the equation of each parabola, we need at least three points on the graph. However, you have only provided two points, (-5, -20) and (4, ?). To determine the equation of the parabola, we would need the second point's y-coordinate as well. Please provide the y-coordinate of the second point, and we will calculate the equations for you.
Answered by
GPT 3.5
To determine the equation of each parabola, we will use the given points (-5, -20) and (4, 20). Let's start with the first parabola.
1st Parabola:
We have two points on the graph: (-5, -20) and (4, 20).
Factored Form:
To find the factored form of the equation, we need to determine the values of the equation in the form: a(x - p)(x - q), where (p, 0) and (q, 0) are the x-intercepts.
From the graph, we can see that the x-intercepts are approximately -3 and 2. Therefore, our equation in factored form is:
f(x) = a(x - (-3))(x - 2)
To find the value of "a", we can substitute the coordinates of one of the given points into the equation and solve for a. Let's use (-5, -20):
-20 = a(-5 - (-3))( -5 - 2)
-20 = a(-5 + 3)(-7)
-20 = a(-2)(-7)
-20 = 14a
a = -20/14
a = -10/7
Hence, the equation of the first parabola in factored form is:
f(x) = (-10/7)(x + 3)(x - 2)
Standard Form:
To convert the equation into standard form, we need to expand and simplify the factored form.
f(x) = (-10/7)(x + 3)(x - 2)
f(x) = (-10/7)(x^2 + x - 6)
f(x) = -10/7 * x^2 - (10/7) * x + (10/7) * 6
f(x) = -10/7 * x^2 - (10/7) * x + 60/7
Hence, the equation of the first parabola in standard form is:
f(x) = -10/7 * x^2 - (10/7) * x + 60/7
Now, let's determine the equation of the second parabola.
2nd Parabola:
We have two points on the graph: (-5, -20) and (4, 20).
Factored Form:
Similar to the first parabola, we can use the same method to find the equation in factored form.
From the graph, it can be observed that the x-intercepts are approximately -2 and 3. Hence, the equation in factored form is:
g(x) = a(x + 2)(x - 3)
To find the value of "a", we can substitute the coordinates of one of the given points into the equation and solve for a. Let's use (-5, -20):
-20 = a(-5 + 2)( -5 - 3)
-20 = a(-3)(-8)
-20 = 24a
a = -20/24
a = -5/6
Therefore, the equation of the second parabola in factored form is:
g(x) = (-5/6)(x + 2)(x - 3)
Standard Form:
To convert the equation into standard form, we expand and simplify the factored form.
g(x) = (-5/6)(x + 2)(x - 3)
g(x) = (-5/6)(x^2 - x - 6)
g(x) = -5/6 * x^2 + (5/6) * x + (5/6) * 6
g(x) = -5/6 * x^2 + (5/6) * x + 5/6 * 6
g(x) = -5/6 * x^2 + (5/6) * x + 5
Hence, the equation of the second parabola in standard form is:
g(x) = -5/6 * x^2 + (5/6) * x + 5
1st Parabola:
We have two points on the graph: (-5, -20) and (4, 20).
Factored Form:
To find the factored form of the equation, we need to determine the values of the equation in the form: a(x - p)(x - q), where (p, 0) and (q, 0) are the x-intercepts.
From the graph, we can see that the x-intercepts are approximately -3 and 2. Therefore, our equation in factored form is:
f(x) = a(x - (-3))(x - 2)
To find the value of "a", we can substitute the coordinates of one of the given points into the equation and solve for a. Let's use (-5, -20):
-20 = a(-5 - (-3))( -5 - 2)
-20 = a(-5 + 3)(-7)
-20 = a(-2)(-7)
-20 = 14a
a = -20/14
a = -10/7
Hence, the equation of the first parabola in factored form is:
f(x) = (-10/7)(x + 3)(x - 2)
Standard Form:
To convert the equation into standard form, we need to expand and simplify the factored form.
f(x) = (-10/7)(x + 3)(x - 2)
f(x) = (-10/7)(x^2 + x - 6)
f(x) = -10/7 * x^2 - (10/7) * x + (10/7) * 6
f(x) = -10/7 * x^2 - (10/7) * x + 60/7
Hence, the equation of the first parabola in standard form is:
f(x) = -10/7 * x^2 - (10/7) * x + 60/7
Now, let's determine the equation of the second parabola.
2nd Parabola:
We have two points on the graph: (-5, -20) and (4, 20).
Factored Form:
Similar to the first parabola, we can use the same method to find the equation in factored form.
From the graph, it can be observed that the x-intercepts are approximately -2 and 3. Hence, the equation in factored form is:
g(x) = a(x + 2)(x - 3)
To find the value of "a", we can substitute the coordinates of one of the given points into the equation and solve for a. Let's use (-5, -20):
-20 = a(-5 + 2)( -5 - 3)
-20 = a(-3)(-8)
-20 = 24a
a = -20/24
a = -5/6
Therefore, the equation of the second parabola in factored form is:
g(x) = (-5/6)(x + 2)(x - 3)
Standard Form:
To convert the equation into standard form, we expand and simplify the factored form.
g(x) = (-5/6)(x + 2)(x - 3)
g(x) = (-5/6)(x^2 - x - 6)
g(x) = -5/6 * x^2 + (5/6) * x + (5/6) * 6
g(x) = -5/6 * x^2 + (5/6) * x + 5/6 * 6
g(x) = -5/6 * x^2 + (5/6) * x + 5
Hence, the equation of the second parabola in standard form is:
g(x) = -5/6 * x^2 + (5/6) * x + 5