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Section 3.3 Quadratic Functions

Section 3.3 Quadratic Functions. Quadratic Functions. Objetives Define and use three forms of the quadratic function . Find the vertex and intercepts of a quadratic function and sketch its graph . Convert one form of a quadratic function to another. Quadratic Functions.

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Section 3.3 Quadratic Functions

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  1. Section 3.3 Quadratic Functions

  2. QuadraticFunctions • Objetives • Define and use threeforms of thequadraticfunction. • Findthevertex and intercepts of a quadraticfunction and sketch itsgraph. • Convertoneform of a quadraticfunctiontoanother

  3. QuadraticFunctions • The rule or equation of a quadratic function is a polynomial of degree 2. • Example of quadratic functions:

  4. QuadraticFunctions • A quadratic function can be written in three different forms: Polynomial Form Transformation Form x-intercept form If a > 0, parabola opens up If a > 0, parabola opens down

  5. QuadraticFunctions • The shape of the graph of a quadratic function is a parabola. Can have 0,1,or 2 x-intercepts A parabola can open upwards or downwards Always has a vertex which can be the minimum or maximum Always has exactly one y-intercept x-intercept vertex Y-intercept minimum minimum maximum

  6. Line of Symmetry y x Line of Symmetry Parabolas have a symmetric property to them. If we drew a line down the middle of the parabola, we could fold the parabola in half. We call this line the line of symmetry. Or, if we graphed one side of the parabola, we could “fold” (or REFLECT) it over, the line of symmetry to graph the other side. The line of symmetry ALWAYS passes through the vertex.

  7. y a > 0 x a < 0 Quadratic Function In any form of the quadratic function… The parabola will open up when the a value is positive. The parabola will open down when the a value is negative.

  8. Quadratic Functions • Polynomial Form: Example: For the function find the vertex and the x and y intercepts. Then sketch the graph. You try with me: Find the vertex, x and y intercepts of the function, then sketch:

  9. Quadratic Functions • Polynomial Form: Step 1: Find the y-intercept To find y-intercept: x = 0 therefore anywhere there’s an x, substitute with a zero. Shortcut: y-intercept = c y-intercept: (0,4)

  10. Quadratic Functions • Polynomial Form: Step 2: Find the x – intercept To find x-intercept: y = 0 therefore anywhere there’s a y, substitute with a zero. You can solve this quadratic equation by factoring or using the quadratic formula. Always try factoring first. x-intercept: (- 2,0)

  11. Quadratic Functions • Polynomial Form: You can also use the quadratic formula to find the x intercepts. x-intercept: (- 2,0)

  12. Quadratic Functions • Polynomial Form: Be Careful!! …Is a negative square root, then there are no x-intercepts …Is equal to 0, then there’s only one x-intercept

  13. Quadratic Functions • Polynomial Form: Step 3: Find the vertex To find vertex: a=1, b=4, c=4 This will give you the x coordinate of the vertex (x,y) So far I have the x-coordinate of the vertex: (-2, y) To find the y coordinate of the vertex, substitute the x coordinate into the original function.

  14. y x Quadratic Function Let's Sketch!! STEP 1: Find the y-intercept y-intercept: (0,4) STEP 2:Find the x-intercept x-intercept: (- 2,0) STEP 3:Find the vertex STEP 4: Opens up or down? Opens up because a > 0

  15. Homework Sketch the following graphs by finding y-intercept, x-intercept, and the vertex. Great Job!!!!!

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