Question

How do you write a quadratic equation with vertex (-1, 4) and point (-3, - 4)?

Answer 1

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

Explanation:

The quadratic equation in vertex form is :`y=a(x-h)^2+k`

where (h,k) are the coords of the vertex and a is a constant.

here the vertex = (-1,4) , so we can write

`y = a(x+1)^2 + 4" and to find a , use (-3,-4")`

substitute x = -3 and y = -4 into the equation.

hence: `a(-3+1)^2 +4 = -4`

`rArr 4a+4 = -4 → 4a = -8 → a = -2`

thus the equation is : `y=-2(x+1)^2 + 4`

or by expanding the bracket we could also have.

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