Answer:
The formula for the quadratic function is [tex]y=5 - \frac{3}{5} \left(x + 2\right)^{2}[/tex].
Step-by-step explanation:
The quadratic function with vertex [tex](h,k)[/tex] is given by [tex]y=a \left(- h + x\right)^{2} + k[/tex].
We know that the vertex is [tex](-2,5)[/tex]. Thus, the formula for the quadratic function is
[tex]y=a \left(x + 2\right)^{2} + 5[/tex]
To find [tex]a[/tex], use the fact that the quadratic function passes through the point [tex]\left(3, -10\right)[/tex] and we solve for [tex]a[/tex].
[tex]-10=a \left(3 + 2\right)^{2} + 5\\a\left(3+2\right)^2+5=-10\\5^2a+5=-10\\25a+5=-10\\25a=-15\\\frac{25a}{25}=\frac{-15}{25}\\a=-\frac{3}{5}[/tex]
Thus, the formula for the quadratic function is [tex]y=5 - \frac{3}{5} \left(x + 2\right)^{2}[/tex].
Answer:
Basically it's the expanded version of the person who already answered. It's -3/5(x)^2-12/5 x+ 13/5
