Chapter 9: Quadratic Equations and Functions Lesson 1: The Function with Equation y = ax 2 Mrs. Parziale

Vocabulary Parabola -- Symmetric -- Minimum -- Maximum -- Vertex -- Axis of Symmetry -- The curve that is the graph of an equation in the form of y=ax 2 +bx+c or y=ax 2. Right half of the curve is a reflection or mirror image of the left half. The line that is drawn through the vertex of the parabola and splits the curve in half. The lowest point on a curve that opens upward. The minimum or maximum point on a curve. The highest point on a curve that opens downward.

General Equation for a Quadratic The graph of y = ax 2, where a ≠ 0, has the following properties. 1.Parabola is symmetric to the ______________________. 2.Vertex is (0, 0) – the origin. 3.When a > 0, the parabola opens ___________________. 4.When a < 0, the parabola opens ___________________. y-axis upward downward The function with equation __________ for a quadratic function forms a __________. parabola

Example 1 xy=2x Vertex is ____________________Line of symmetry __________ Parabola opens _______________Minimum or maximum? _______ Graph y = 2x 2 (0, 0) x = 0 minupward

Example 2 x Vertex is ____________________Line of symmetry __________ Parabola opens _______________Minimum or maximum? _______ Graph (0, 0) x = 0 maxdownward

Example 3 Match each table with the graph it most accurately represents.

Example 4 Given the function f(x) = -x 2, find x when f(x) = -4. If (2.5, -6.25) lies on the parabola, what are the coordinates of the reflected image over the y-axis?

Closure What type of curve is formed from y=x 2 ? What is the vertex? What is the line of symmetry? Name three points on the graph. Does it open upward or downward? What point becomes the maximum or the minimum?