Question

What is the vertex form, f(x) = a(x − h)2 + k, for a parabola that passes through the point (4, −3) and has (5, 2) as its vertex. What is the standard form of the equation?

A) Vertex form: f(x) = 5(x + 5)2 + 2
Standard form: f(x) = 5x2 + 50x − 123
B) Vertex form: f(x) = 5(x − 5)2 + 3
Standard form: f(x) = 5x2 + 50x − 123
C) Vertex form: f(x) = −5(x − 5)2 + 2
Standard form: f(x) = −5x2 + 50x − 123
D) Vertex form: f(x) = −5(x − 5)2 − 3
Standard form: f(x) = −5x2 + 50x − 148

Answer 1

C

Explanation:

Answer 2

Given that the vertex (h, k) is (5, 2), you know the vertex form will look like
f(x) = a(x -5)² +2
for some value of "a" that makes f(4) = -3. That value of "a" can be found by substituting the given values in the above equation for f(x) and solving for "a".
-3 = a(4 -5)² +2
-3 -2 = a×1²
a = -5

This means the appropriate choice is ...
C) Vertex form: f(x) = -5(x -5)² +2; Standard form: -5x² +50x -123