Find the equation

Question

Write an equation for the quadratic graphed below x-intercepts: (-3,0) and (1,0). Y-intercept: (0,2)

Answer 1

If the x-intercepts are -3 and 1, then the factored form is y = a(x + 3)(x - 1). To find "a", we plug in the data point (x, y) of (0, 2) so:

2 = a(0 + 3)(0 - 1)

2 = -3a

a = -2/3

So the equations is y = -2/3(x + 3)(x - 1)

You COULD (but don't need to) put it in standard form by multiplying it out:

y = -2/3(x² + 2x - 3)

y = -2/3x² - 4/3x + 2