VertexForm of Quadratic Equations Mr Barker Vertex Form

Vertex-Form of Quadratic Equations Mr. Barker

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

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. a=1 y = (x – 2)2 + 5 vertex at (2, 5) y = 4(x – 6)2 – 3 y = 4(x – 6)2 + – 3 a=4 vertex at (6, – 3) y = – 0. 5(x + 1)2 + 9 y = – 0. 5(x – – 1)2 + 9 a = – 0. 5 vertex at (– 1, 9)

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 – 7, 3) 2 vertex at ( b. y = 2(x + 7) +3 – 12) – 2 vertex at (5, c. y = 3(x – 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 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

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)? substitute y = a·(x – h)2 + k simplify 0 = a·(7 – 3)2 + 4 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