Lesson 1-7Lesson 1-7

Quadratic Quadratic Functions and Functions and Their GraphsTheir Graphs

Objective:

Objective:

To define and graph

quadratic functions.

Quadratic Function:

Quadratic Function:

f(x) = ax2 + bx +c where a 0.

Quadratic Function:

f(x) = ax2 + bx +c where a 0.

The graph of a quadratic

function is called a parabola.

Special Parts of a Parabola:

Special Parts of a Parabola:

Vertex: The turning point. It is either a

maximum or minimum.

Special Parts of a Parabola:

Axis of Symmetry: A vertical line that passes through the

vertex.

http://2012books.lardbucket.org/books/elementary-algebra/section_12_05.html

Special Parts of a Parabola:

Axis of Symmetry: This line is midway between the x-intercepts

therefore it is the “average” of the x-values.

http://2012books.lardbucket.org/books/elementary-algebra/section_12_05.html

Axis of Symmetry:

Axis of Symmetry:

Can always be found by

calculating the formula

Vertex:

Vertex:

Can always be found using the

formula

Discriminant:

Discriminant:• If b2 – 4ac > 0

Parabola crosses x-axis twice. There will be two x-intercepts.

Discriminant:• If b2 – 4ac > 0

Parabola crosses x-axis twice. There will be two x-intercepts.

• If b2 – 4ac = 0Parabola is tangent to the

x-axis. There is only one x-intercept.

Discriminant:• If b2 – 4ac > 0

Parabola crosses x-axis twice. There will be two x-intercepts.

• If b2 – 4ac = 0Parabola is tangent to the

x-axis. There is only one x-intercept.

• If b2 – 4ac < 0Parabola never crosses the x-axis so there are no x-intercepts.

Find the intercepts, axis of Find the intercepts, axis of symmetry, and the vertex of symmetry, and the vertex of

the given parabola.the given parabola.

y = (x + 4)(2x – 3)y = (x + 4)(2x – 3)

Now sketch the graph.Now sketch the graph.

Sketch the graph of the parabola. Label Sketch the graph of the parabola. Label the intercepts, the axis of symmetry, the intercepts, the axis of symmetry,

and the vertex.and the vertex.

y = 2xy = 2x22 – 8x + 5 – 8x + 5

If the equation can be written in the form of :

If the equation can be written in the form of :

then the vertex of the parabola is (h, k) and the axis of symmetry is the equation

x = h.

Find the vertex of the Find the vertex of the parabola by completing the parabola by completing the

square.square.

y = -2xy = -2x22 + 12x + 4 + 12x + 4

Now, find the x- and y-Now, find the x- and y-intercepts.intercepts.

y = -2xy = -2x22 + 12x + 4 + 12x + 4

Find the equation of the quadratic Find the equation of the quadratic function function ff with with ff(-1) = -7 and a (-1) = -7 and a maximum value maximum value ff(2) = -1. Show (2) = -1. Show

that the function has no that the function has no xx-intercepts.-intercepts.

Where does the line y = 2x + 5 intersect the parabola y = 8 – x2?

*Show this both algebraically and graphically.

Find an equation of the function whose graph is a parabola with x-intercepts 1

and 4 and a y-intercept of -8.

General Linear Function:

So far we know

f(x) = dx + ebut we also know

y = mx + bwhere m = slope.

What is the slope of What is the slope of y = y = ¼¼ x x - 3- 3??

Assignment:Assignment:

Pgs. 40-41Pgs. 40-41C.E.C.E. 1-6 all 1-6 all

W.E.W.E. 1-25 (Left Column) 1-25 (Left Column)