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# April 4, 2014

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### April 4, 2014

1. 1. Holt Algebra 1 9-3 Graphing Quadratic Functions TGIF April 4, 2014 Today:  Review from Yesterday  Getting to Know the Quadratic Function: (how the b value changes the parabola)  Class Work
2. 2. Holt Algebra 1 9-3 Graphing Quadratic Functions Important Concepts from Yesterday: 1. There is no single "right way" to graph a quadratic function. In fact the goal is for you to understand and use a variety of methods, so that you can choose the best (easiest) method for a given problem. 2. The axis of symmetry is an important part of parabolas and can save you much time and effort if you understand its properties. Because a parabola is symmetrical, each point is the same number of units away from the axis of symmetry. Helpful Hint 2.5 You must have at least 5 points to graph the parabola.
3. 3. Holt Algebra 1 9-3 Graphing Quadratic Functions 4. The vertex is an (x,y) coordinate on the AOS, and is either the minimum or maximum y value Important Concepts from Yesterday: 5. The vertex is an (x,y) coordinate on the AOS, and is either the minimum or maximum y value 6. All parabolas begin from the parent function (y = x2), and are moved around the coordinate plane from changes in the a, b, and c values. 3. The axis of symmetry has a single coordinate (x) and represents the exact center of the parabola. 7. A quadratic equation with no solutions will not cross the x-axis at any point. It can still be graphed using other methods.
4. 4. Holt Algebra 1 9-3 Graphing Quadratic Functions Review from Yesterday: How the a and c values affect the quadratic function y = ax2 + bx + c Start with the parent function, which is... First, how does a change in a affect the parabola y = x2 Effects of the a, b, & c values
5. 5. Holt Algebra 1 9-3 Graphing Quadratic FunctionsEffects of the a, b, & c values 1. The greater the value of 'a', the narrower and steeper the graph. 2. A positive 'a' value results in parabola which turns up and has a vertex minimum. 3. A negative 'a' value results in parabola which turns down and has a vertex maximum.
6. 6. Holt Algebra 1 9-3 Graphing Quadratic FunctionsEffects of the a, b, & c values How does a change in c affect the parabola? The value of c is also used to find the y-intercept. Set the 'x' values = 0, and find the intercept. We would expect the value of 'c' in this graph to be.......
7. 7. Holt Algebra 1 9-3 Graphing Quadratic Functions Effects of the a, b, & c values How changes in 'b' affect the parabola: Why does a positive b value (see aqua, b = 2) result in a shift 2 units to the left?
8. 8. Holt Algebra 1 9-3 Graphing Quadratic Functions Graph the quadratic function. y = x2 + 4x + 4 Step 2 Find the axis of symmetry, Step 1: Try to picture what the graph will look like before you start. Use the a,b, and c values to determine your prediction Step 3: Determine the best method(s) to solve that particular function. Step 4 : Plot at least 5 points, then connect the dots to complete the parabola. then find 'y' to complete the coordinates for the vertex
9. 9. Holt Algebra 1 9-3 Graphing Quadratic Functions Step 2 Find the axis of symmetry and the vertex. y = x2 + 4x + 2 Substitute for x to find the y coordinate The x-coordinate of the vertex is... The y-coordinate is Find at least 4 more points, then graph. This is also the AOS
10. 10. Holt Algebra 1 9-3 Graphing Quadratic Functions Step 5 Graph the axis of symmetry, the vertex, the point containing the y-intercept, and two other points. Step 6 Reflect the points across the axis of symmetry. Connect the points with a smooth curve. y = x2 + 4x + 2 Example 2 Continued
11. 11. Holt Algebra 1 9-3 Graphing Quadratic Functions Class Work: Graphing Quadratic Functions
12. 12. Holt Algebra 1 9-3 Graphing Quadratic Functions