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Understanding X-Intercepts and the Quadratic Formula in Quadratic Functions

This chapter focuses on solving quadratic equations using the quadratic formula and finding their x-intercepts. The quadratic formula applies when the equation is in the form ax² + bx + c = 0. Key concepts include the discriminant, which provides insight into the nature of the solutions. By analyzing the discriminant (b² - 4ac), we determine whether the solutions are imaginary, real, rational, or irrational. Additionally, we explore the vertex of a parabola associated with the quadratic function.

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Understanding X-Intercepts and the Quadratic Formula in Quadratic Functions

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  1. 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. 186 #1-35 Every other odd

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