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Chapter 4

Chapter 4. Section 4-10 Writing Equations: 1. Vertex Point plus another Point 2. Quadratic Regression. Objectives. I can write the equation of a quadratic function given the vertex and another point I can find the equation to any quadratic function given at least 3 points. Vertex Format.

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Chapter 4

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  1. Chapter 4 Section 4-10 Writing Equations: 1. Vertex Point plus another Point 2. Quadratic Regression

  2. Objectives • I can write the equation of a quadratic function given the vertex and another point • I can find the equation to any quadratic function given at least 3 points

  3. Vertex Format • Recall that vertex format for any quadratic equation is given by: • y = a (x – h)2 + k • Where (h, k) is the vertex point

  4. Finding the Equation • If we know the vertex of a parabola, then we know h and k • Then if we know any other point, we know an x and y value, so we can solve for “a” in the equation

  5. Writing an Equation in Vertex Format

  6. Example 1 • Find the equation of the parabola with vertex (3, -4) and goes through point (0, 1) • y = a(x – h)2 + k • There are 5 variables here: a, h, k, x, y • We know 4 of the 5, so we can solve for “a”

  7. Vertex (3, -4) and Point (0, 1)

  8. Vertex (3, 1) and Point (6, 3)

  9. Example 3 • Write the equation in Standard Vertex Format for the parabola that passes thru point (2, 1) and has a vertex point (-2, -3) • y = a(x – h)2 + k • 1 = a(2 - -2)2 + -3 • 1 = a(4)2 – 3 • 1 = 16a – 3 • 4 = 16a • a = 1/4

  10. Example 4 • Write the equation in Standard Vertex Format for the parabola that passes thru point (-3, -5) and has a vertex point (4, 1) • y = a(x – h)2 + k • -5 = a(-3 - 4)2 + 1 • -5 = a(-7)2 + 1 • -5 = 49a + 1 • -6 = 49a • a = -6/49

  11. Quadratic Regression • If we know 3 points on a parabola, then we can use quadratic regression and find the equation using the calculator • Given we know the following 3 ordered pairs that are on the parabola • (1, 2), (4, 3), and (7, 6) • Write the equation : y = ax2 + bx + c

  12. STAT Button • 3rd row • 3rd button

  13. Entering Data

  14. STAT Button • 3rd row • 3rd button

  15. Calculating the Equation

  16. Possible Errors • Enter wrong number into L1 or L2 • Forget a negative sign • Forget to clear L1 or L2 • Use a list other than L1 and L2

  17. Example 1 • Find the equation of the parabola that passes through the following points • (-1, -1), (1, 11), (3, 7) • STAT • EDIT • Enter the L1 data {-1, 1, 3} • Enter L2 data {-1, 11, 7} • Now STAT to Calc #5 Quad Reg then ENTER • y = -2x2 + 6x + 7

  18. Homework • WS 6-5

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