Presentation on theme: "Objectives: To solve quadratic equations using the Quadratic Formula. To determine the number of solutions by using the discriminant."— Presentation transcript:
Objectives: To solve quadratic equations using the Quadratic Formula. To determine the number of solutions by using the discriminant.
By Completing the Square of the following you will derive the Quadratic Formula. ax² + bx + c = 0
Solve by using the quadratic equation: A. Write in standard form: (Set = to zero, like when factoring ) B. Divide by the common multiple, if there is one C. Identify a, b, and c. Then evaluate by using the quadratic formula.
II. Discriminant Solutions to a quadratic are its x-intercepts. How many x-intercepts does a parabola have? Two interceptsOne interceptNone
So, a parabola can have zero, one, or two x- intercepts. How can we know the numbers of x-intercepts without graphing?
A. The Discriminant: b 2 - 4ac If b 2 - 4ac > 0, then there are two x- intercepts(two real solutions) If b 2 - 4ac = 0, then there is one x- intercept(one solution—double root) If b 2 - 4ac < 0, then there are NO x- intercepts(no real solutions - two conjugate imaginary roots)
B. Evaluate the discriminant and describe the number and type of roots. 1. y = x 2 + 2x – 3 2.y = x 2 + 4x + 4 3.y = x 2 + x + 5