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Definitions 4/23/2017 Quadratic Equation in standard form is viewed as, ax2 + bx + c = 0, where a ≠ 0 Parabola is a u-shaped graph If a is positive, it opens up If a is negative, it opens down Vertex is the highest or lowest point of the graph Axis of Symmetry is the vertical line passing through the vertex (the “x” of vertex) it is represented by a DASHED-line Roots/Zeros are the solutions to the Quadratic it is where the graph crosses the x-axis. Also known as the minimum or maximum value

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Definitions 4/23/2017 y = x2 – 4 Roots: The solutions to the equation . Also known as the zeros X-intercept(s): Point(s) where the graph crosses the x-axis. Ordered Pair: (–2, 0) Ordered Pair: (2, 0) Vertex: Minimum or maximum value Axis of Symmetry: Line that separates the graph in half; always written as x = ______

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**To graph a Quadratic Equation**

1st find the Vertex a. find the x-coordinate of the vertex by using the vertex formula. b. Substitute the x-value into the Quadratic equation to find the y-value of the vertex. Write the vertex as an ordered pair. (x, y) The x-value of the vertex ALSO gives the Axis of Symmetry. Write the Axis of Symmetry as an equation. x =__

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**2nd find the Roots…when y=0.**

***where the graph crosses the x-axis*** a. Set the equation = to 0 b. Factor the equation. c. Solve each factor for x.

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**Example 1 Given equation: Find the vertex The x-value of vertex is:**

4/23/2017 Given equation: Find the vertex The x-value of vertex is: The y-value of vertex: Vertex: Axis of symmetry: Minimum/maximum:

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**Example 1 Find the Roots Set the equation = 0 Factor the equation**

4/23/2017 Find the Roots Set the equation = 0 Factor the equation Solve for x Roots:

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**Example 1 Vertex: Axis of symmetry: Roots: What is the Domain?**

Is the vertex a minimum or maximum point? Minimum at y = –9 Vertex: y-intercept: Axis of symmetry: Roots: Reflection over axis of symmetry No reflection What is the Domain? What is the Range?

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**Example 2 Given equation: vertex y-coordinate Axis of symmetry**

Roots (y=0) 1 solution Min/max? Min at y = 0 Find the y-intercept (x=0) Domain Reflection over axis of symmetry Range 8

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**Example 3 Given equation: vertex y-coordinate Axis of symmetry**

y-intercept: Given equation: Reflection over axis of symmetry vertex No reflection y-coordinate Axis of symmetry Roots (y=0) Min/max? Min at y = -2 Domain Range

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**Your turn Given equation, y = 2x2 – 2x + 5 Determine: up How it opens**

4/23/2017 Given equation, y = 2x2 – 2x + 5 Determine: How it opens Y-Intercept The Vertex Axis of Symmetry Domain Range Minimum/Maximum up (0, 5) (0.5, 4.5) x = 0.5 All Real Numbers y > 4.5 No solution Min at 4.5

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