Question

Write the function in vertex form.

A) p(x) = 4x² - 24x - 15
B) p(x) = 4(x - 3)² - 99
C) p(x) = 4(x + 3)² - 9
D) p(x) = 4x² + 24x - 15

Answer 1

To find the vertex form of a quadratic function, we can use the formula h = -b / (2a) for the x-coordinate of the vertex, and k = c - (b² / 4a) for the y-coordinate of the vertex.

Step-by-step explanation:

The function in vertex form is given by:

p(x) = a(x - h)² + k

where (h, k) is the vertex of the parabola. To find the vertex form, we can use the formula:

h = -b / (2a)

k = c - (b² / 4a)

Let's calculate the vertex form for each option:

A) p(x) = 4x² - 24x - 15

h = -(-24) / (2*4) = 3

k = -15 - (-24² / 4*4) = -15 - 144/16 = -24.25

Therefore, the vertex form for option A is p(x) = 4(x - 3)² - 24.25

Using the same process, we find the vertex forms for the other options:

B) p(x) = 4(x - 3)² - 99

C) p(x) = 4(x + 3)² - 9

D) p(x) = 4x² + 24x - 15

Based on the calculations, option C is the correct answer.