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Warm Up

Learn how to expand binomials and understand different forms of quadratic equations including vertex form and standard form. Explore the vertex form equation to find the coordinates of the vertex and create quadratic equations with specific vertex points. Practice finding the value of 'a' in the equation for different parabolas by using the vertex and other given points. Complete classwork assignments and homework exercises to reinforce your understanding.

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Warm Up

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  1. Expand the following pairs of binomials: (x-4)(2x+3) (3x-1)(x-11) (x+8)(x-8) Warm Up

  2. Quadratics Equations Standard Form, Vertex Form and Graphing

  3. Vertex Form of a Quadratic Equation • Recall that the standard form of a quadratic equation is y = a·x2 + b·x + c where a, b, and c are numbers and adoes not equal 0. • The vertex form of a quadratic equation is y = a·(x – h)2 + k where (h, k) are the coordinates of the vertex of the parabola and a is a number that does not equal 0.

  4. Vertex Form of a Quadratic Equation • Vertex form y = a·(x – h)2 + k allows us to find vertex of the parabola without graphing or creating a x-y table. y = (x – 2)2 + 5 a = 1 vertex at (2, 5) y = 4(x – 6)2 –3 a = 4 vertex at (6, –3) y = 4(x – 6)2 +–3 y = –0.5(x + 1)2 +9 a = –0.5 vertex at (–1, 9) y = –0.5(x – –1)2 +9

  5. Vertex Form of a Quadratic Equation • Check your understanding… 1. What are the vertex coordinates of the parabolas with the following equations? vertex at (4, 1) a. y = (x – 4)2 + 1 vertex at (–7, 3) b. y = 2(x + 7)2 + 3 vertex at (5, –12) c. y = –3(x – 5)2– 12 2. Create a quadratic equation in vertex form for a "wide" parabola with vertex at (–1, 8). y = 0.2(x + 1)2+ 8

  6. Vertex Form of a Quadratic Equation • Finding the a value. • Recall that the vertex form of a quadratic equation is y = a·(x – h)2 + k where (h, k) are the coordinates of the vertex of the parabola and a is a number that does not equal 0. Also, the values of x and y represent the coordinates of any point (x, y) that is on the parabola. • We can see that (2, 9) is a point on y = (x – 4)2 + 5 9 = (2 – 4)2 + 5 9 = 4 + 5 …because the equation is true 9 = 9

  7. Vertex Form of a Quadratic Equation • Finding the a value (cont'd) • If we know the coordinates of the vertex and some otherpointon the parabola, then we can find the a value. • For example, What is the a value in the equation for a parabola that has a vertex at (3, 4) and an x-intercept at (7, 0)? y = a·(x – h)2 + k substitute 0 = a·(7 – 3)2 + 4 simplify 0 = a·(4)2 + 4 simplify 0 = a·16 + 4 subtract 4 -4 = a·16 divide by 16 -0.25 = a y = -0.25·(x – 3)2 + 4

  8. Vertex Form of a Quadratic Equation • Finding the a value (cont'd) What is the a value in the equation for a parabola that has a vertex at (2, -10) and other point at (3, -15)?

  9. Vertex Form of a Quadratic Equation • Classwork assignment • A particular parabola has its vertex at (-3, 8) and an x- • intercept at (1, 0). Your task is to determine which of • the following are other points on that same parabola. • 1. (-1, 6) • 2. (0, 3) • 3. (4, -16) • 4. (5, -24)

  10. Homework: Page 199: 23-37 odd and 55, 57

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