Question

Write a formula for quadratic function if its graph has the vertex at point (−2,5) and passes through the point (3,−10).

Answer 1

Answer:

The formula for the quadratic function is $y=5 - \frac{3}{5} \left(x + 2\right)^{2}$.

Step-by-step explanation:

The quadratic function with vertex $(h,k)$ is given by $y=a \left(- h + x\right)^{2} + k$.

We know that the vertex is $(-2,5)$. Thus, the formula for the quadratic function is

$y=a \left(x + 2\right)^{2} + 5$

To find $a$, use the fact that the quadratic function passes through the point $\left(3, -10\right)$ and we solve for $a$.

$-10=a \left(3 + 2\right)^{2} + 5\\a\left(3+2\right)^2+5=-10\\5^2a+5=-10\\25a+5=-10\\25a=-15\\\frac{25a}{25}=\frac{-15}{25}\\a=-\frac{3}{5}$

Thus, the formula for the quadratic function is $y=5 - \frac{3}{5} \left(x + 2\right)^{2}$.