1. Section 5-3: X-intercepts and the Quadratic Formula
CHAPTER 5:
QUADRATIC FUNCTIONS
AND COMPLEX NUMBERS
Section 5-3:
X-intercepts and the
Quadratic Formula

2. Objective
Given a quadratic equation, solve it using the quadratic formula, and use the result to find the x-intercepts of the quadratic function.

3. The Quadratic Formula
If a quadratic equation has the form: ax2 + bx + c then the solutions are:

4. Solve the Following Examples:

5. The Discriminant
If ax2 + bx + c = 0, then the quantity b2 – 4ac is called the discriminant.
We use the discriminant to determine the nature of solutions of a quadratic equation.

6. The Nature of Solutions
Given ax2 + bx + c = 0, where a, b, and c are real numbers:
If b2 – 4ac is:
Negative, then the equation has solutions with imaginary numbers.
Positive, then the equation has real-number solutions.
If the positive number is a perfect square, then the solutions are rational.
If the positive number is not a perfect square, then the solutions are irrational.

7. Vertex of a Parabola
If ax2 + bx + c, then the x- coordinate of the vertex is:

8. Find the Vertex

9. HOMEWORK:
p #1-35
Every other odd