Answer: [tex]\bold{y=-\dfrac{1}{4}(x-3)^2+2}[/tex]
Step-by-step explanation:
The vertex form of a quadratic equation is: y = a(x - h)² + k, where
- (h, k) is the vertex
- "a" is the vertical stretch
Input the vertex (3, 2) and the point (-1, -2) into the equation to solve for "a":
[tex]-2 = a(-1-3)^2+2\\\\-2=a(-4)^2+2\\\\-2=16a+2\\\\-4=16a\\\\\dfrac{-4}{16}=\dfrac{16}{16}a\\\\-\dfrac{1}{4}=a[/tex]
Now, input the vertex and the a-value into the equation:
[tex]y=-\dfrac{1}{4}(x-3)^2+2[/tex]
