Question

.Write the quadratic equation in standard form that
has x-intercepts at (-4/3,0) and (-3,0)

Answer 1

y = a(x² + (13/3)x + 12/3)

Explanation:

First use the equation in x-intercept form: y = a(x-r)(x-s)

Where r and s are the values for the x-intercept

Substitute the x-intercepts

y = a(x - (-4/3)) (x - (-3))

Simplify

y = a(x + (4/3)) (x + 3)

Distributive property for brackets:

y = a(x² + 3x + (4/3)x + 12/3)

Find common denominator in fractions to collect like terms

y = a(x² + (9/3)x + (4/3)x + 12/3)

y = a(x² + (13/3)x + 12/3)

We cannot solve for the "a" value without another point.

If given the other point, substitute it for x and y to solve for a.

Then rewrite the equation with the "a" value.