Graphing Quadratic Equations SECTION 1.1. WHAT IS A QUADRATIC EQUATION? An equation of the form: y = ax 2 + bx + c (a, b, and c are constants) When graphed,

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Presentation transcript:

Graphing Quadratic Equations SECTION 1.1

WHAT IS A QUADRATIC EQUATION? An equation of the form: y = ax 2 + bx + c (a, b, and c are constants) When graphed, a quadratic equation forms a U-shaped pattern called a parabola. Compare y = x 2, y = 2x 2, and y = -1/4x What similarities and differences do you see in the graphs?

AXIS OF SYMMETRY Every parabola has an axis of symmetry, which is a vertical line that goes through the vertex and cuts the parabola in half. Look at the following equations and their corresponding axes of symmetry. Can you figure out how the axis is calculated based on the equation?

TRY TO FIGURE OUT THE PATTERN….. x 2 + 4x – 6axis: x = 2x 2 + 8x – 6axis: x = 3x 2 – 6x – 8axis: x = 3x 2 – 3x + 10axis: x = -x 2 + 8x + 2axis: x = Don’t forget the equations we already looked at that have an axis of symmetry of 0.

CHARACTERISTICS OF Y = AX 2 + BX + C

STEPS FOR GRAPHING 1. Identify the coefficients a, b, and c. 2. Find the vertex. Find the x-coordinate first by calculating –b/2a. Then substitute that x-coordinate into the equation to find the y-coordinate. 3. Draw the axis of symmetry. 4. Plot the y-intercept, (0, c). 5. Evaluate the function for other values of x, and use the symmetry of the graph to plot more points. 6. Connect the points to make a smooth curve.

EXAMPLES Graph the following equations. y = x 2 – 2x – 3 y = -x 2 + 6x + 8 y = 2x 2 + 6x + 3

REAL-WORLD APPLICATION A video store sells about 150 DVDs a week at a price of $20 each. The owner estimates that for each $1 decrease in price, about 25 more DVDs will be sold each week. How can the owner maximize weekly revenue?