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Understanding Quadratic Functions: Real-World Applications & Graphing Techniques

Learn about quadratic functions, their importance in various industries like painting, roofing, landscaping, and more. Explore standard form and graphing methods for parabolas. Practice examples and get ready to solve problems!

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Understanding Quadratic Functions: Real-World Applications & Graphing Techniques

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  1. Quadratic Function Parabola Next

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  4. Quadratic function • What is a quadratic function? • It is a polynomial expression of degree 2. • Why do we need to study quadratic functions? • Painting business • Roof business • Landscape business • Astronomy • Car repair business Next Prev

  5. More examples of quadratic functions in the real world Next Prev

  6. Quadratic functions Standard form: x2 y x2 c or a + = f(x) + c a = a c Where: = coefficient = constant Next Prev

  7. Quadratic functions Graphing a quadratic function: Option 1 : Make a table of values (T-table) Place the ordered pairs on the coordinate plane Join the points with a smooth curve The graph is also called a Parabola Option 2 : Transform the equation into y=ax2 + c Use the calculator Next Prev

  8. Quadratic functions Example: Graph: y = x2 Y 4 4 y=(-2)2 => y= 4 4 -2 1 1 -1 y=(-1)2 => y= 1 1 -X X 0 0 y=(0)2 => y= 0 0 1 y=(1)2 => y= 1 1 2 y=(2)2 => y= 4 4 -Y Next Prev

  9. Quadratic functions Y U-shape ==========> (+) ==========>Parabola (up) -X X -Y Next Prev

  10. Quadratic functions Now is your turn!!! Get your books on page 452 problems 2-8 Prev

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