Write an equation for the parabola in standard form.

Question

Write an equation for the parabola in standard form.

 

Answer 1

X-intercepts @ (-5, 0) and (-3, 0)

Vertex: (-4, 4)

The x-intercepts are considered zeros (solutions). We will change them into factors.

x = -5 → x + 5 = 0

x = -3 → x + 3 = 0

y = a(x + 5)(x + 3)

Since the parabola opens downward, the "a" term is negative. Let's plug in the values of the vertex into the equation to find a.

a(-4 + 5)(-4 + 3) = 4

a(1)(-1) = 4

-a = 4

a = -4

Since the quadratic equation is in factored form, we need to convert it into standard form.

y = -4(x + 5)(x + 3)

y = -4(x² + 3x + 5x + 15)

y = -4(x² + 8x + 15)

y = -4x² - 32x - 60

Answer 2

We loking for equation in vertex form: f(x) = a(x + 4)² + 4;

To get a we use x-intercept (- 3, 0), so 0 = a(- 3 + 4)² + 4, a = - 4.

Equation of parabola f(x) = - 4(x + 4)² + 4