Answer:
y = 1
Step-by-step explanation:
Given:
- equation of the parabola: [tex]y=a(x-1)^2+q[/tex]
- points on the parabola: (-1, -9) and (1, 1)
Substitute point (1, 1) into the given equation of the parabola to find q:
[tex]\begin{aligned}\textsf{At}\:(1,1)\implies a(1-1)^2+q &=1\\a(0)^2+q &=1\\q &=1\end{aligned}[/tex]
Substitute the found value of q and point (-1, -9) into the given equation of the parabola to find a:
[tex]\begin{aligned}\textsf{At}\:(-1,-9)\implies a(-1-1)^2+1 &=-9\\a(-2)^2+1 &=-9\\4a+1 &=-9\\4a &=-10\\a &=-\dfrac{5}{2}\end{aligned}[/tex]
Therefore, the equation of the parabola is:
[tex]y=-\dfrac{5}{2}(x-1)^2+1[/tex]
The maximum or minimum point on a parabola is the vertex.
Vertex form of a parabola: [tex]y=a(x-h)^2+k[/tex] where (h, k) is the vertex.
Therefore, the vertex of the parabola is (1, 1) and so the maximum value of y = 1
