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Fireworks – Vertex Form of a Quadratic Equation

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

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Fireworks – Vertex Form of a Quadratic Equation

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  1. Fireworks – 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.

  2. Fireworks – 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

  3. Fireworks – 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

  4. Fireworks – 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

  5. Fireworks – Vertex Form of a Quadratic Equation • Finding the a value (cont'd) • If we know the coordinates of the vertex and some otherpoint on 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

  6. Fireworks – 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)?

  7. Fireworks – 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)

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