Final answer:
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.