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# Unit 10 – Quadratic Functions - 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

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### Unit 10 – Quadratic Functions

• Standard form:
• Graph: parabola
What is the vertex of a quadratic function?
• Highest or lowest point
• Vertex: (-1, -6)
• y-value is called minimum
• Parabola opens upward (a > 0)
What is the vertex of a quadratic function?
• Vertex: (1, 7)
• y-value is called maximum
• Parabola opens downward (a < 0)
Finding domain & range
• Domain: ALWAYS all real #
• Range: ALWAYS an inequality
• y coordinate of vertex represents minimum or maximum value of range
• Range: y ≥ -6
Finding domain & range
• Domain: all real #
• Range: y ≤ 7
What is the axis of symmetry?
• Vertical line that divides parabola in half
• REMEMBER: equation for a vertical line is x = a
• a of s: x = -1
Finding axis of symmetry algebraically
• 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.

Using axis of symmetry to find vertex
• 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).

What are the zeros of a quadratic function?
• 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
Determining a Function From a Graph
• 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)
Determining a Function From a Graph
• Using standard form of a quadratic equation, write a system of equations.
• REMEMBER: We already have a value for c(from y-intercept).
Determining a Function From a Graph
• 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.

Determining a Function From a Graph

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