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

Quadratics Equations Standard Form, Vertex Form and Graphing

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 where (h, k) are the coordinates of the vertex of the parabola and a is a number that does not equal 0.

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 + 5a = 1 vertex at (2, 5) y = 4(x – 6) 2 – 3a = 4 vertex at (6, – 3) y = 4(x – 6) 2 + – 3 y = – 0.5(x + 1) 2 + 9a = – 0.5 vertex at ( – 1, 9) y = – 0.5(x – – 1) 2 + 9

Vertex Form of a Quadratic Equation Check your understanding… 1.What are the vertex coordinates of the parabolas with the following equations? a. y = (x – 4) b. y = 2(x + 7) c. y = – 3(x – 5) 2 – 12 vertex at (4, 1) vertex at ( – 7, 3) vertex at (5, – 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

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 anypoint (x, y) that is on the parabola. We can see that (2, 9) is a point on y = (x – 4) = (2 – 4) = = 9 …because the equation is true

Vertex Form of a Quadratic Equation Finding the a value (cont'd) If we know the coordinates of the vertex and some other point 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 0 = a·(7 – 3) = a·(4) = a· = a· = a substitute simplify subtract 4 divide by 16 y = -0.25·(x – 3) 2 + 4

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)?

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)

Homework: Page 199: odd and 55, 57