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## Graphing Quadratic Functions

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**Graphing Quadratic Functions**Lesson 9.3A Algebra 2**Quadratic Function**The standard form of a quadratic function is written: where a≠0 and a, b, and c are constants.**Sketching a Quadratic Function**• The graph of a quadratic function is a U-shaped curve called a parabola. • If the leading coefficient a is positive, then the parabola opens up. • If the leading coefficient a is negative, then the parabola opens down.**Minimum and Maximum**• If the vertex is the lowest point of the parabola, then it is a minimum. • If the vertex is the highest point of the parabola, then it is a maximum.**Axis of Symmetry**The line passing through the vertex that divides the parabola into two symmetric parts. The two parts are mirror images of each other (reflections) about the line of symmetry.**Graph of a Quadratic Function**• The graph of y = ax2 + bx + c is a parabola. • If a is positive, then the parabola opens up. • If a is negative, then the parabola opens down. • The vertex has an x-coordinate of • The axis of symmetry is the vertical line**Graphing a Quadratic Function**• Find the x-coordinate of the vertex. • Find the y-coordinate of the vertex by plugging the x-coordinate into the quadratic equation and solving for y. • Make a table of values, using the x-values to the left and to the right of the vertex. • Plot the points and connect them with a smooth curve to form a parabola. Example: y = 2x2 + 3x +4**Example**Sketch the graph of y = -4x2 – 3x + 2 End of Lesson**Using a Quadratic Model in a Real-Life Problem**Lesson 9.3B Algebra 2**Using a Quadratic Modelp. 522, # 65**Path of the dolphin jumping out of the water: h = -0.2d2 + 2d h = height out of the water, d = horizontal distance Our plan: The maximum height reached by the dolphin is the y-coordinate of the vertex. First, we need to find the x-coordinate of the vertex, then plug that value into the original quadratic equation to find the y-value.**Using a Quadratic Modelp. 522, # 65**h = -0.2d2 + 2d so, a = -0.2, b = 2 The dolphin reached a maximum height of 5 feet out of the water.**p. 522, #66**How far did the dolphin jump? Hint: Remember that a parabola is a reflection about the line of symmetry End of Lesson