Graphing Quadratic Functions
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The document discusses how to graph quadratic functions by finding the axis of symmetry, vertex, and y-intercept. It explains that the axis of symmetry is located at x = -b/2a, which is the x-coordinate of the vertex. Once the vertex x-coordinate is identified, you can plug it back into the function to find the vertex y-coordinate. The y-intercept is simply the constant term c. It also briefly mentions that for quadratic inequalities, the region will be shaded above or below the parabola depending on whether it is greater than or less than the function.
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Graphing Quadratic Functions
- 2. Find the Axis of Symmetry The axis of symmetry is located at x = –b/2a Can you think of a way of remembering –b/2a besides memorizing it? Memorizing it is a good idea. This is also the x coordinate of the vertex.
- 3. Find the Axis of Symmetry Find the axis of symmetry for y = 5 – 4x – x 2 - (-4)/2(-1) x = -2
- 4. Find the Vertex Now that you know the x coordinate for the vertex, you can plug it into your function and solve for y y = 5 – 4(-2) – (-2) 2 y = 9 The vertex is located at (-2,9)
- 5. Find the y-intercept This part is easy What is x when the graph crosses y? Make x = 0 and solve for y What do you notice? The y-intercept is c!
- 6. Graphing Quadratic Inequalities Based on what we know about linear inequalities, where will we shade if: y > ax 2 + bx + c y < ax 2 + bx + c