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Unit 10 – Quadratic Functions

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Unit 10 – Quadratic Functions

Topic: Characteristics of Quadratic Functions

- Standard form:
- Parent quadratic function:
- 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.

Check your equation on your graphing calculator.

Homework

Complete the handout you received in class. Be prepared to present solutions on the board.

DUE 4/16 (A-day) or 4/17 (B-day)