Vertex and Intercept Form of Quadratic Function

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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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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.

### Vertex Form of the Quadratic

Determine the vertex of the following functions:

f(x) = 2(x – 1)2 + 1

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

h(x) = 3(x – 2)2 – 7

Vertex & Axis of Symmetry Summary
• Put equation in standard form f(x) = ax2 + bx + c
• Determine the value “a” and “b”
• Determine if the graph opens up (a > 0) or down (a < 0)
• Find the axis of symmetry:
• Find the vertex by substituting the “x” into the function and solving for “y”
• 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 – 1)2 + 1

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

h(x) = 3(x – 2)2 – 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 – h)2 + k, where:
• The vertex is located at (h, k)
• The axis of symmetry is x = h
• The “a” is the same as in the standard form
• The “a” 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 – h)2 + k

Vertex Shift HORIZONTAL amount

In Class:
• Do page 63 of Note Taking Guide
• Do first 6 problems of Henley Task Day 2 – be sure to graph the y = x2 for each graph.
In Class
• Do page 64 of the Note Taking Guide
• Do Day 2 of the Henley Task, # 4a – 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 – 3)(x – 1)

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

h(x) = -3(x – 2)(x + 3)

Determine the x-intercepts (zero prod rule)

Find the axis of symmetry (average)

Find “y” value of the vertex (sub into f(x))

V = (-0.5, 18.75)

Homework
• Page 65, # 1, 2, and 19 – 22 all
Convert from Standard to Vertex Form
• Standard: MM2A3a Students will
• Convert between standard and vertex form.
Convert from Standard to Vertex Forms
• We converted from Vertex form to Standard form of the quadratic function above in slide 3 by expanding the

(a – h)2 term and combining like terms

• How can we convert from Standard form to Vertex form?
Convert from Standard to Vertex Forms
• Look at the standard form:

y = ax2 + bx + c, where a ≠ 0

• And look at the Vertex form:

y = a(x – h)2 + k

• “h” is the axis of symmetry, which is the “x” part of the coordinates of the vertex
• “k” is the “y” part of the vertex
Convert from Standard to Vertex Forms
• How did we find the axis of symmetry?
• This is the “h” of the vertex form
• How did we then find the “y” part of the vertex?
• Substitute the x into the original equation and solve for y.
• This is the “k” of the vertex form
• The “a” is the same for both forms
Convert from Standard to Vertex Forms
• Convert the following functions to vertex form:
• f(x) = x2 + 10x – 20
• y = (x + 5)2 - 45
• g(x) = -3x2 – 3x + 10
• y = -3(x + 0.5)2 + 10.75
• h(x) = 0.5x2 – 4x – 3
• y = 0.5(x – 4)2 - 11