BELLWORK Determine whether the following function has a

BELL-WORK Determine whether the following function has a maximum or minimum value. Explain your answer. y = 2 x 2 – 16 x + 24 Minimum; the leading coefficient is positive What is the maximum/minimum value of the function? Minimum occurs at x = -(-16) 2(2) x=4 Minimum is 2(4)2 – 16(4) + 24 = -8 When will it occur? Minimum occurs when x = 4.

The Graph of a Quadratic What are the coordinates of the vertex of the parabola represented by y = (x + 10)2 – 64? Using the format y = a(x – h)2 + k, y = (x + 10)2 – 64 is written as: y = (x – (-10))2 +(- 64) Vertex = (-10, -64)

The Graph of a Quadratic What are the coordinates of the vertex of the parabola represented by y = (x + 10)2 – 64? Is the parabola a maximum or a minimum? Minimum (The leading coefficient is positive) What is the equation of the axis of symmetry? x = -10 (The vertex is the lowest point on the axis of symmetry. Since the vertex has coordinates (-10, -64), the equation of the vertical line passing through that point is x = -10).

The Graph of a Quadratic What are the coordinates of the vertex of the parabola represented by y = (x + 10)2 – 64? What are the coordinates of the x-intercepts? x-intercepts occur where y = 0 0 = (x + 10)2 – 64 64 = (x + 10)2 +8 = x + 10 ***when you square 8 and -8 the result is 64 x = -10 + 8 x = -2 or -18 (-2, 0) & (-18, 0)

The Graph of a Quadratic What are the coordinates of the vertex of the parabola represented by y = (x + 10)2 – 64? What are the coordinates of the y-intercepts? y-intercept occur where x = 0 y = (0 + 10)2 – 64 y = 36 (0, 36) Sketch it!

Completing the Square Write y = x 2 + 20 x + 36 in vertex form by completing the square. First ensure that the value of A is 1. Find half of B 10 and square it 100 Add and subtract this figure to the quadratic so that it stays balanced y = x 2 + 20 x +100 – 100 + 36 Notice that we have not changed the original quadratic. Consider x 2 + 20 x + 100 Factor it! = (x + 10)2

Completing the Square So y = x 2 + 20 x + 100 – 100 + 36 can be re-written as: y = (x + 10)2 – 100 + 36 y = (x + 10)2 – 64 Vertex: (-10, -64) AOS: x = -10 x-int: (-2, 0) & (-18, 0) y-int: (0, 36)

Graphing a Quadratic from Vertex Form Sketch the graph y = x 2 + 9 x – 136 Write it in vertex form: y = x 2 + 9 x + 81 – 81– 136 4 4

Graphing a Quadratic from Vertex Form Sketch the graph y = x 2 + 9 x – 136 Write it in vertex form: y = x 2 + 9 x + 81 – 81– 136 4 4 y =

Graphing a Quadratic from Vertex Form Sketch the graph y = x 2 + 9 x – 136 Write it in vertex form: y = x 2 + 9 x + 81 – 81– 136 4 4 y =

Graphing a Quadratic from Vertex Form y= Coordinates of the vertex:

Graphing a Quadratic from Vertex Form

Graphing a Quadratic from Vertex Form

Graphing a Quadratic from Vertex Form

Graphing a Quadratic from Vertex Form

Graphing a Quadratic from Vertex Form

Graphing a Quadratic from Vertex Form

Graphing a Quadratic from Vertex Form

Graphing a Quadratic from Vertex Form