Chapter 4 Quadratic Functions and Factoring - 4.10 Write Quadratic Functions and Models - 4.10 Exercises - Skill Practice - Page 312: 12

$y=-\frac{3}{4}(x-2)^{2}+1$

We already know $y$, $x$, $k$ and $h$ from the given vertex and point, so in order to get the quadratic function we need to find $a$... $y=a(x-h)^{2}+k$ $-2=a(4-2)^{2}+1$ $-3=a(2)^{2}$ $4a=-3$ $a=-\frac{3}{4}$ Therefore the function is... $y=-\frac{3}{4}(x-2)^{2}+1$