Find the rule of a quadratic function whose graph has the given vertex and passes through the given point.
-vertex $(3,-4)$; point $(2,-7)$
A) $f(x)=(x-3)^{2}-4$
B) $f(x)=2(x-3)^{2}-4$
C) $f(x)=-3(x-3)^{2}-4$
D) $f(x)=-3(x+3)^{2}-4$

Question

Quizplus · Accepted Answer

The vertex form of a quadratic function is $f(x) = a(x-h)^2 + k$, where $(h, k)$ is the vertex. Given the vertex $(3, -4)$, the function is $f(x) = a(x-3)^2 - 4$. Using the point $(2, -7)$, substitute into the equation to find $a$: $-7 = a(2-3)^2 - 4$. Solving gives $a = -3$, so the function is $f(x) = -3(x-3)^2 - 4$.

Find the Rule of a Quadratic Function Whose Graph Has (3,−4)(3,-4)(3,−4)

Find the Rule of a Quadratic Function Whose Graph Has $(3,-4)$