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# Vertex and Intercept Form of Quadratic Function - PowerPoint PPT Presentation

Vertex and Intercept Form of Quadratic Function. Standard: MM2A3c Students will Investigate and explain characteristics of quadratic functions, including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema , intervals of increase, and decrease, and rates of change .

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Standard: MM2A3c Students will

Investigate and explain characteristics of quadratic functions, including domain, range, vertex, axis of

symmetry, zeros, intercepts,

extrema, intervals of

increase, and decrease,

and rates of change.

### Vertex Form of the Quadratic

Determine the vertex of the following functions:

f(x) = 2(x β 1)2 + 1

g(x) = -(x + 3)2 + 5

h(x) = 3(x β 2)2 β 7

• Put equation in standard form f(x) = ax2 + bx + c

• Determine the value βaβ and βbβ

• Determine if the graph opens up (a > 0) or down (a < 0)

• Find the axis of symmetry:

• Find the vertex by substituting the βxβ into the function and solving for βyβ

• Determine two more points on the same side of the axis of symmetry

• Graph the axis of symmetry, vertex, & points

### Vertex Form of the Quadratic

V = (1, 1)

V = (-3, 5)

V = (2, -7)

Determine the vertex of the following equations:

f(x) = 2(x β 1)2 + 1

g(x) = -(x + 3)2 + 5

h(x) = 3(x β 2)2 β 7

Compare the equations and the vertices. Do you notice a pattern?

The x part is the opposite sign of the number inside the brackets and the y part is the same as the number added or subtracted at the end.

• The vertex form of the quadratic equation is of the form:

• y = a(x β h)2 + k, where:

• The vertex is located at (h, k)

• The axis of symmetry is x = h

• The βaβ is the same as in the standard form

• The βaβ is the stretch of the function

• The vertex is shifted right by h

• The vertex is shifted up by k

From y = x2

Stretch factor Vertex Shift VERTICAL amount

y = a(x β h)2 + k

Vertex Shift HORIZONTAL amount

• Do page 63 of Note Taking Guide

• Do first 6 problems of Henley Task Day 2 β be sure to graph the y = x2 for each graph.

• Do page 64 of the Note Taking Guide

• Do Day 2 of the Henley Task, # 4a β 4e all

### Intercept Form of the Quadratic Function

V = (2, -1)

V = (-2.5, -4.5)

How can we determine the vertex of the following equations without putting them in standard form?

f(x) = (x β 3)(x β 1)

g(x) = 2(x + 1)(x + 4)

h(x) = -3(x β 2)(x + 3)

Determine the x-intercepts (zero prod rule)

Find the axis of symmetry (average)

Find βyβ value of the vertex (sub into f(x))

V = (-0.5, 18.75)

• Page 65, # 1, 2, and 19 β 22 all

• Standard: MM2A3a Students will

• Convert between standard and vertex form.

• We converted from Vertex form to Standard form of the quadratic function above in slide 3 by expanding the

(a β h)2 term and combining like terms

• How can we convert from Standard form to Vertex form?

• Look at the standard form:

y = ax2 + bx + c, where a β  0

• And look at the Vertex form:

y = a(x β h)2 + k

• βhβ is the axis of symmetry, which is the βxβ part of the coordinates of the vertex

• βkβ is the βyβ part of the vertex

• How did we find the axis of symmetry?

• This is the βhβ of the vertex form

• How did we then find the βyβ part of the vertex?

• Substitute the x into the original equation and solve for y.

• This is the βkβ of the vertex form

• The βaβ is the same for both forms

• Convert the following functions to vertex form:

• f(x) = x2 + 10x β 20

• y = (x + 5)2 - 45

• g(x) = -3x2 β 3x + 10

• y = -3(x + 0.5)2 + 10.75

• h(x) = 0.5x2 β 4x β 3

• y = 0.5(x β 4)2 - 11