1 / 17

- PowerPoint PPT Presentation

Unit 10 – Quadratic Functions. Topic: Characteristics of Quadratic Functions. What is a quadratic function?. Standard form: Parent quadratic function: Graph: parabola. What is the vertex of a quadratic function?. Highest or lowest point Vertex: (-1, -6) y -value is called minimum

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

PowerPoint Slideshow about '' - crevan

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

• Standard form:

• Graph: parabola

• Highest or lowest point

• Vertex: (-1, -6)

• y-value is called minimum

• Parabola opens upward (a > 0)

• Vertex: (1, 7)

• y-value is called maximum

• Parabola opens downward (a < 0)

• Domain: ALWAYS all real #

• Range: ALWAYS an inequality

• y coordinate of vertex represents minimum or maximum value of range

• Range: y ≥ -6

• Domain: all real #

• Range: y ≤ 7

• Vertical line that divides parabola in half

• REMEMBER: equation for a vertical line is x = a

• a of s: x = -1

• Formula:

• Example: Find the axis of symmetry for the function

Plug in values for a (2) & b (–8) & simplify. WATCH YOUR SIGNS!

Axis of symmetry for this function is the vertical line x = 2. SIGN NOTE: Notice the two negatives cancel. Remember the formula includes a negative.

• Finding vertex coordinates:

• x-coordinate: axis of symmetry

• y-coordinate: substitute x-coordinate into function & simplify

We’ve already found the x-coordinate (2). Replace x in the function with 2 & solve for y.

Vertex for this function is the point (2, –11).

• x-value(s) that makes function = 0

• Using graph: zeros are the points where the parabola crosses x-axis

• Two real zeros

• x = -1 and x = 2

• one real zero

• x = 1

• No real zeros

• Identify 3 points from the graph.

• One should be the y-intercept; pick points that make the math easy.

• (0, 6), (2, 0), (3, 0)

• Using standard form of a quadratic equation, write a system of equations.

• REMEMBER: We already have a value for c(from y-intercept).

• Simplify & solve for a & b.

Divide 1st equation by -2. Divide 2nd equation by 3. Add equations to eliminate b.

Plug the value of a into one of the equations & solve for b.

Write the function in standard form with the values of a, b & c.