vertex is (2,-1) and y intercept is (0,7) find the quadratic equation

Answer 1

Assume a quadratic equation of the form:

y=a*x^2+b*x+c

Use the y-intercept:

(7)=a*(0)^2+b*(0)+c

c=7

y = a*x^2+b*x+7

The derivative of the quadratic at its vertex is 0:

dy/dx = 2*a*x+b

dy/dx(x=2)=0=2*a*(2)+b

a=-b/4

y=-b/4 * x^2 + b*x+7

Use the vertex coordinates to solve for b:

(-1)=-b/4*(2)^2+b*(2)+7

-1=-b/4 *4 + 2*b +7

-8=-b+2b

b=-8

a=-b/4

a=-(-8)/4=2

Substituting a and b:

y=2*x^2-8x+7

This is the quadratic equation with a vertex at (2,1) and the y-intercept at (0,7)