Question

Write the equation for the parabola that has x− intercepts (−2,0) and (4,0) and y− intercept (0,4).

Answer 1

Answer:

$y = -\frac{1}{2}(x^2-2x-8)$

Simplified it is $y=-\frac{1}{2}x^2+x+4$

Step-by-step explanation:

The x-intercepts of a parabola form the factors of the equation. Since the x -intercepts are (-2,0) and (4,0) then the factors are (x+2) and (x-4). Factors are pieces which multiply to make the equation.

$y=(x+2)(x-4)\\y=x^2+2x-4x-8\\y=x^2-2x-8$

This is the standard form of the parabola $ax^2+bx+c$. Since the y-intercept of the parabola is (0,4) then a number must also be multiplied to it

$y=a(x^2-2x-8)$

We find a by plugging in x=0 and y=4.

$4=a(0^2-2(0)-8)\\4=a(0-0-8)\\4=a(-8)\\\frac{4}{-8} = a\\\frac{-1}{2} = a$

So the equation is $y = -\frac{1}{2}(x^2-2x-8)$.

When simplified it is $y=-\frac{1}{2}x^2+x+4$