write a quadratic function in standarrd form whose graphe passes through (-8,0),(1,0),(2,3)

Answer 1

Fortunately we are given the 2 zeros (-8 and 1) so (x-1) and (x+8) are factors

so we can write this as a(x-1)(x+8) = a(x^2 +7x -8). We can use the point (2,3) to solve for a

3= a( (2)^2 +7(2) -8))

3= a(4+14-8)

3= 10a

a=3/10

So our equation is

f(x)= (3/10)(x^2 +7x -8)

If you graph this equation you will see it passes through the 3 given points

Answer 2

y = .3*(x+3.5)^2-6.075

This comes from an expansion of the root equation y = (x-2)(x-1)(x+8) and then solving for the constants & vertex.