Question

Identify the vertex of y=4(x−25)2−61 .
Show your work
Answer
Identify the vertex of y=4(x−25)^2−61 .
Show your work.
Answer
Identify the vertex of y=4(x−25)2−61 .
Explain your work
Answer
Identify the vertex of y=4(x−25)2−61 .
Show me how you got it
Answer
Determine the zero(s) of the quadratic function y=6x2+13x+5 . Show all steps.
Answered by GPT 3.5
The equation is in the form y = a(x-h)^2 + k, where (h,k) represents the vertex of the parabola.

Comparing the given equation, y = 4(x-25)^2 - 61, with this form, we can see that the vertex is at (h,k) = (25, -61).

Therefore, the vertex of y = 4(x-25)^2 - 61 is (25, -61).
Answered by GPT 3.5
To identify the vertex of the equation y = 4(x-25)^2 - 61, we can directly compare it with the general vertex form of a parabola: y = a(x-h)^2 + k, where (h,k) represents the vertex.

In this case, we can see that the parabola is already in the vertex form with h = 25 and k = -61.

Therefore, the vertex of y = 4(x-25)^2 - 61 is (25, -61).
Answered by GPT 3.5
To identify the vertex of the equation y = 4(x-25)^2 - 61, we can use the vertex formula for parabolas of the form y = a(x-h)^2 + k, where (h, k) represents the coordinates of the vertex.

In the given equation, we have (h, k) = (25, -61) as the vertex.

The equation tells us that the vertex is located at the point (25, -61), so the vertex of y = 4(x-25)^2 - 61 is (25, -61).
Answered by GPT 3.5
To identify the vertex of the equation y = 4(x-25)^2 - 61, we can use the vertex formula for parabolas of the form y = a(x-h)^2 + k, where (h, k) represents the coordinates of the vertex.

In this case, the equation is already in the form y = 4(x-25)^2 - 61, so we can directly read the values of h and k.

Comparing the given equation with the vertex form, we have h = 25 and k = -61.

Therefore, the vertex of y = 4(x-25)^2 - 61 is (25, -61).
Answered by GPT 3.5
To determine the zeros of the quadratic function y = 6x^2 + 13x + 5, we need to find the values of x for which y is equal to zero.

Step 1: Set y = 0
0 = 6x^2 + 13x + 5

Step 2: Factor or use the quadratic formula to solve for x.

Since the equation does not easily factor, we will use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In our case, a = 6, b = 13, and c = 5.

x = (-13 ± √(13^2 - 4*6*5)) / (2*6)
x = (-13 ± √(169 - 120)) / 12
x = (-13 ± √49) / 12
x = (-13 ± 7) / 12

So we have two possible solutions:
x = (-13 + 7) / 12 = -6/12 = -1/2
x = (-13 - 7) / 12 = -20/12 = -5/3

Therefore, the zeros of the quadratic function y = 6x^2 + 13x + 5 are x = -1/2 and x = -5/3.