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Unit 10 – Quadratic Functions

Unit 10 – Quadratic Functions. Topic: Characteristics of Quadratic Functions. What is a quadratic function?. Standard form: Parent quadratic function: Graph: parabola. What is the vertex of a quadratic function?. Highest or lowest point Vertex: (-1, -6) y -value is called minimum

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Unit 10 – Quadratic Functions

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  1. Unit 10 – Quadratic Functions Topic: Characteristics of Quadratic Functions

  2. What is a quadratic function? • Standard form: • Parent quadratic function: • Graph: parabola

  3. What is the vertex of a quadratic function? • Highest or lowest point • Vertex: (-1, -6) • y-value is called minimum • Parabola opens upward (a > 0)

  4. What is the vertex of a quadratic function? • Vertex: (1, 7) • y-value is called maximum • Parabola opens downward (a < 0)

  5. Finding domain & range • Domain: ALWAYS all real # • Range: ALWAYS an inequality • y coordinate of vertex represents minimum or maximum value of range • Range: y ≥ -6

  6. Finding domain & range • Domain: all real # • Range: y ≤ 7

  7. What is the axis of symmetry? • Vertical line that divides parabola in half • REMEMBER: equation for a vertical line is x = a • a of s: x = -1

  8. Finding axis of symmetry algebraically • Formula: • Example: Find the axis of symmetry for the function Plug in values for a (2) & b (–8) & simplify. WATCH YOUR SIGNS! Axis of symmetry for this function is the vertical line x = 2. SIGN NOTE: Notice the two negatives cancel. Remember the formula includes a negative.

  9. Using axis of symmetry to find vertex • Finding vertex coordinates: • x-coordinate: axis of symmetry • y-coordinate: substitute x-coordinate into function & simplify We’ve already found the x-coordinate (2). Replace x in the function with 2 & solve for y. Vertex for this function is the point (2, –11).

  10. What are the zeros of a quadratic function? • x-value(s) that makes function = 0 • Using graph: zeros are the points where the parabola crosses x-axis • Two real zeros • x = -1 and x = 2

  11. What are the zeros of a quadratic function? • one real zero • x = 1

  12. What are the zeros of a quadratic function? • No real zeros

  13. Determining a Function From a Graph • Identify 3 points from the graph. • One should be the y-intercept; pick points that make the math easy. • (0, 6), (2, 0), (3, 0)

  14. Determining a Function From a Graph • Using standard form of a quadratic equation, write a system of equations. • REMEMBER: We already have a value for c(from y-intercept).

  15. Determining a Function From a Graph • Simplify & solve for a & b. Divide 1st equation by -2. Divide 2nd equation by 3. Add equations to eliminate b. Plug the value of a into one of the equations & solve for b.

  16. Determining a Function From a Graph Write the function in standard form with the values of a, b & c. Check your equation on your graphing calculator.

  17. Homework Complete the handout you received in class. Be prepared to present solutions on the board. DUE 4/16 (A-day) or 4/17 (B-day)

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