Question

Write an equation given the he vertex form and a point. vertex(3,2)and pass through the point(-1 -2)

Answer 1

Answer:
`\bold{y=-(1)/(4)(x-3)^2+2}`

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":

`-2 = a(-1-3)^2+2\\\\-2=a(-4)^2+2\\\\-2=16a+2\\\\-4=16a\\\\(-4)/(16)=(16)/(16)a\\\\-(1)/(4)=a`

Now, input the vertex and the a-value into the equation:

`y=-(1)/(4)(x-3)^2+2`