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Instructions and examples for graphing quadratic equations and identifying their symmetries with respect to the x-axis, y-axis, and origin. It includes exercises for determining the x- and y-intercepts of various equations and identifying which equations are symmetric with respect to different axes or the origin.
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1. Sketch the graph of the equation. y = 2 x โ 3 Submission Data line: 2*x- Label the x - and y -intercepts. (If an answer does not exist, enter DNE.) x -intercept ( x , y ) = y -intercept ( x , y ) = 2. Sketch the graph of the equation. y = โ x^2 + 2 parabola: -x^2+ Label the x - and y -intercepts. (If an answer does not exist, enter DNE.) x -intercept ( x , y ) = (smaller x -value) x -intercept ( x , y ) = (larger x -value) y -intercept ( x , y ) = Practice Another Version
3. Sketch the graph of the equation. y = x^3 Label the x - and y -intercepts. (If an answer does not exist, enter DNE.) x -intercept ( x , y ) = Practice Another Version 1 10
Label the x - and y -intercepts. (If an answer does not exist, enter DNE.) x -intercept ( x , y ) = y -intercept ( x , y ) =
5. Use tests for symmetry to determine which graphs from the lists below are symmetric with respect to the y -axis, the x -axis, and the origin. (Select all that apply.) (a) symmetric with respect to the y -axis y = 8 x โ 3 y = โ x + 8 y = โ8 x^2 y = 7 x^2 โ 2 x = 1/4 y^2 x = โ y^2 + 2 y = โ1/9 x^3 y = x^3 โ 9
y =sqrt(x) โ 6 (b) symmetric with respect to the x -axis y = 8 x โ 3 y = โ x + 8 y = โ8 x^2 y = 7 x^2 โ 2 x = 1 4 y^2 x = โ y^2 + 2 y = โ 1 9 x^3 y = x^3 โ 9 y = x y = x x x
d 81 x^2 = 64 x = 8. Solve the equation by using the following special quadratic equation. (Enter your answers as a comma- separated list. If there is no solution, enter NO SOLUTION.)
d ( x โ 3 )^2 = 15 x = Practice Another Version Practice Another Version
