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

Apr 8, 2016

$y = - 2 {\left(x + 1\right)}^{2} + 4$

#### Explanation:

The quadratic equation in vertex form is :$y = a {\left(x - h\right)}^{2} + k$

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: $a {\left(- 3 + 1\right)}^{2} + 4 = - 4$

rArr 4a+4 = -4 → 4a = -8 → a = -2

thus the equation is : $y = - 2 {\left(x + 1\right)}^{2} + 4$

or by expanding the bracket we could also have.

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