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Understanding Quadratic Functions: Graphing Properties and Vertex Calculation

This section delves into the properties of quadratic functions, which can be represented in standard form. It explains how the graph of a quadratic function is a parabola that can either open upwards (concave up) or downwards (concave down), depending on the coefficient of the squared term. Key features such as x-intercepts, y-intercept, and vertex are discussed, along with methods to find them. The importance of real solutions is highlighted, including scenarios with two, one, or no real solutions, assisting readers in graphing quadratic functions effectively.

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Understanding Quadratic Functions: Graphing Properties and Vertex Calculation

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Presentation Transcript

  1. Section 7.5 – Graphing Quadratic Functions Using Properties

  2. Quadratic Function A function that can be written in the form , where is a quadratic function. The graph of a quadratic function is a parabola. opens up Concave Up x-intercept y-intercept vertex

  3. Quadratic Function - Concavity

  4. Quadratic Function - Concavity If a > 0, concave up If a < 0, concave down Matching

  5. Quadratic Function – y-intercept

  6. Quadratic Function – y-intercept y-intercept: (0, c) Matching

  7. Quadratic Function – x-intercepts Can’t be factored using real numbers

  8. Quadratic Function – x-intercepts The x-intercepts of are the REAL solutions to the quadratic equation. Two Real Solutions No Real Solutions One Real Solution

  9. Quadratic Function – x-intercepts

  10. Finding the Vertex – Standard Form The vertex of the parabola is an ordered pair, (h, k). It can be found by finding the x value first: Once you have found the x value, substitute that value in to the function and simplify to find the y value.

  11. Finding the Vertex - Standard Form Vertex:

  12. Finding the Vertex - Standard Form Vertex:

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