Question

Write an equation for the quadratic graphed below:

x-intercepts: (-3,0) and (1,0); y-intercept: (0,-3)

Answer 1

• y = (x + 3)(x - 1) or y = x² + 2x - 3

Explanation:

Quadratic equation:

• y = a(x - p)(x - q), where a - constant, p and q - x-intercepts.

Substitute p and q:

• y = a(x - (-3))(x - 1)
• y = a(x + 3)(x - 1)

Find the value of a, using the y-intercept:

• - 3 = a(0 + 3)(0 - 1)
• - 3 = a*3*(-1)
• -3 = - 3a
• a = 1

The equation is:

• y = (x + 3)(x - 1)

or

• y = x² + 2x - 3