# Quadratic Functions and Their Graphs

## Presentation on theme: "Quadratic Functions and Their Graphs"— Presentation transcript:

Lesson 1-7 Quadratic Functions and Their Graphs

Objective:

To define and graph quadratic functions.
Objective: To define and graph quadratic functions.

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

The graph of a quadratic function is called a parabola.
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.

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.

Axis of Symmetry:

Can always be found by calculating the formula
Axis of Symmetry: Can always be found by calculating the formula

Vertex:

Can always be found using the formula
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 = 0 Parabola 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 = 0 Parabola is tangent to the x-axis. There is only one x-intercept. If b2 – 4ac < 0 Parabola never crosses the x-axis so there are no x-intercepts.

Find the intercepts, axis of symmetry, and the vertex of the given parabola. y = (x + 4)(2x – 3)

Now sketch the graph.

Sketch the graph of the parabola
Sketch the graph of the parabola. Label the intercepts, the axis of symmetry, and the vertex. y = 2x2 – 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 parabola by completing the square
Find the vertex of the parabola by completing the square. y = -2x2 + 12x + 4

Now, find the x- and y-intercepts. y = -2x2 + 12x + 4

Find the equation of the quadratic function f with f(-1) = -7 and a maximum value f(2) = -1. Show that the function has no x-intercepts.

Where does the line y = 2x + 5 intersect the parabola y = 8 – x2
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 + e but we also know y = mx + b where m = slope.

What is the slope of y = ¼ x - 3?

Assignment: Pgs. 40-41 C.E. 1-6 all W.E. 1-25 (Left Column)