9.4 the Quadratic Formula Earlier we looked at how to solve quadratic equations in the form of ax2 + c = 0 by taking the square root. We are going to look at how to solve ANY quadratic equation in standard form of ax2 + bx + c = 0 To do this, we use the QUADRATIC FORMULA. No one knows who discovered it, but versions of it go back as far as 2000 B.C. in Babylonia (4,000 yrs. ago)

QUADRATIC FORMULA. X = -b +- b2 – 4ac 2a To use the quadratic formula, your equation must be in standard form. Tells you what the x-intercepts of the equation are. With a quadratic equation, you may have 2 x-intercepts, 1, or none. (see graphs) X = -b +- b2 – 4ac 2a

Using the quadratic equation Coefficient of x2 is the “a”, coefficient of x is the “b”, and what’s being added is the “c” Solve using the quadratic formula X2 + 5x – 14 = 0 X = 2 & -7

To graph a quadratic equation Find the vertex Use the quadratic formula to find the x-intercepts. If there are no x-intercepts, choose an x-value to the right & to the left of the vertex & solve for y

graph Find the vertex & use the quadratic formula to find the x-intercepts X2 + 8x + 12 = 0 -x2 + 4 = 0

Homework out