1. Graphing Quadratic Equations A-SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. A-REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). F-IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. A-REI.4 Solve quadratic equations in one variable. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p) 2 = q that has the same solutions. Derive the quadratic formula from this form. Solve quadratic equations by inspection (e.g., for x 2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b. F-BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

2. Graphing in Standard Form

3. Parts of a Parabola from Graph Parabola: the graph of a quadratic equation (u shape) Axis of symmetry: the vertical line that goes through the vertex Vertex: the highest or lowest point of a parabola (where the parabola changes direction) Minimum: graph will have “u” shape (valley) Maximum: graph will have “n” shape (hill)

4. Parts of a Parabola from Graph X-intercepts: (roots/zeroes) point(s) where graph crosses or touches the x-axis Y-intercept: point where the parabola crosses the y-axis Domain: x values of the graph – Read graph from left to right Range: y values of the graph – Read graph from bottom to top

5. Parts of a Parabola

6. Examples Use the graphs below to determine the vertex, axis of symmetry, min/max, x-intercept, y- intercept, domain and range. 1. 2.

7. Parts of a Parabola from Equation

8. Examples

9. Graphing in Vertex Form

10. Transformations in Vertex Form

12. Examples

13. Vertex Form to Standard Form

14. Standard Form to Vertex Form METHOD 1: Identify the values of a, b, and c. Find the vertex of the parabola. Substitute the values of a and the vertex into the equation for vertex form. Simplify. METHOD 2: Group first two terms together Factor out a Complete the square Subtract equivalent value at the end of the equation

15. Examples

16. Writing Equations from Graphs Substitute the x and y coordinates of the vertex in the place of h and k in the vertex formula Choose another point on the graph and substitute into the formula for x and y Solve the equation for a and substitute into the vertex formula

17. Writing Equations from Graphs