Vertex and intercept form of quadratic function l.jpg
This presentation is the property of its rightful owner.
Sponsored Links
1 / 16

Vertex and Intercept Form of Quadratic Function PowerPoint PPT Presentation


  • 167 Views
  • Uploaded on
  • Presentation posted in: General

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 .

Download Presentation

Vertex and Intercept Form of Quadratic Function

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Vertex and intercept form of quadratic function l.jpg

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 l.jpg

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 l.jpg

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 quadratic4 l.jpg

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.


Vertex form of the quadratic5 l.jpg

Vertex Form of the Quadratic

  • 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


Vertex form of the quadratic6 l.jpg

Vertex Form of the Quadratic

From y = x2

Stretch factor Vertex Shift VERTICAL amount

y = a(x – h)2 + k

Vertex Shift HORIZONTAL amount


In class l.jpg

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 class9 l.jpg

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 l.jpg

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 l.jpg

Homework

  • Page 65, # 1, 2, and 19 – 22 all


Convert from standard to vertex form l.jpg

Convert from Standard to Vertex Form

  • Standard: MM2A3a Students will

  • Convert between standard and vertex form.


Convert from standard to vertex forms l.jpg

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 forms14 l.jpg

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 forms15 l.jpg

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 forms16 l.jpg

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


  • Login