Section 5-3: X-intercepts and the Quadratic Formula

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Presentation transcript:

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

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

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

Solve the Following Examples:

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.

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.

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

Find the Vertex

HOMEWORK: p. 186 #1-35 Every other odd