Algebra II ElementsAlgebra II Elements5.2: Graph quadratic function in 5.2: Graph quadratic function in

vertex or intercept formvertex or intercept form

HW: p.232 (36-48 even)HW: p.232 (36-48 even)

Tomorrow: projects are due, midterm Tomorrow: projects are due, midterm review.review.

Vertex FormVertex Form y = a(x – h)y = a(x – h)22 + k + k

Vertex: (h, k)Vertex: (h, k) Line of symmetry: x = h.Line of symmetry: x = h.

Steps in graphing:Steps in graphing:1.) Plot vertex (h, k). 1.) Plot vertex (h, k).

2.) chart and plot points.2.) chart and plot points.

Graph y = 2(x – 4)Graph y = 2(x – 4)22 – 1 – 1XX

YY

Graph y = (x + 1)Graph y = (x + 1)22 + 3 + 3XX

YY

Graph y = -2(x + 1)Graph y = -2(x + 1)22 + 3 + 3XX

YY

Intercept formIntercept form Steps in graphing intercept formSteps in graphing intercept form

y = a(x – p)(x – q)y = a(x – p)(x – q) Plot the x-intercepts: points p and qPlot the x-intercepts: points p and q x-coord of vertex = average p & q.x-coord of vertex = average p & q.

Find y-coordinate of vertex by plugging in. Find y-coordinate of vertex by plugging in. Plot the vertex.Plot the vertex.

Graph y = (x + 2)(x – 2)Graph y = (x + 2)(x – 2)

Graph y = 3(x + 3)(x + 5)Graph y = 3(x + 3)(x + 5)

Graph y = -2(x + 1)(x – 2)Graph y = -2(x + 1)(x – 2)

3 types of graphs3 types of graphs1.) Standard Form: 1.) Standard Form: y = axy = ax22 + bx + c + bx + c

1.) x-coordinate of vertex: 1.) x-coordinate of vertex: 2.) chart with vertex in the middle2.) chart with vertex in the middle

2.) Vertex Form: y = a(x – h)2.) Vertex Form: y = a(x – h)22 + k + k1.) vertex: (h, k)1.) vertex: (h, k)2.) chart with vertex in the middle2.) chart with vertex in the middle

3.) Intercept Form: 3.) Intercept Form: y = a(x – p)(x – q)y = a(x – p)(x – q)1.) x-intercepts: p and q1.) x-intercepts: p and q

2.) x-coordinate of vertex: average 2.) x-coordinate of vertex: average p and q. Find y by plugging in.p and q. Find y by plugging in.

Graph 1.) Graph 1.) y = (x – 4)(x – 2)y = (x – 4)(x – 2)2.) 2.) y = 3xy = 3x22

Graph 3.) y = -2xGraph 3.) y = -2x22 + 5 + 54.) 4.) y = (x – 2)y = (x – 2)22

Graph 5.) y = 1/2(x + 1)(x – 2)Graph 5.) y = 1/2(x + 1)(x – 2)6.) 6.) f(x) = -xf(x) = -x22 - 2x - 1 - 2x - 1

Graph 7.) Graph 7.) y = 3xy = 3x22 + 6x – 4 + 6x – 48.) 8.) y = ½xy = ½x22