![]() ![]() This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission. Graph the parabola using the points found. Point symmetric to the y-intercept is ( 2, −3 ). The point one unit to the right of the line of symmetry is ( 2, −3 ) ( 2, −3 ) The point ( 0, −3 ) ( 0, −3 ) is one unit to the left of the line of symmetry. To find the axis of symmetry, find x = − b 2 a x = − b 2 a. You may want to choose two more points for greater accuracy. Since the value of the discriminant is negative, there is no solution and so no x- intercept.Ĭonnect the points to graph the parabola. Point symmetric to the y- intercept is ( −4, 5 ) ( −4, 5 ). The point two units to the left of the line of symmetry is ( −4, 5 ). The point ( 0, 5 ) ( 0, 5 ) is two units to the right of the line of symmetry. ![]() To find the axis of symmetry, find x = − b 2 a. Now, we can use the discriminant to tell us how many x-intercepts there are on the graph.īefore you start solving the quadratic equation to find the values of the x-intercepts, you may want to evaluate the discriminant so you know how many solutions to expect. ![]() Previously, we used the discriminant to determine the number of solutions of a quadratic equation of the form a x 2 + b x + c = 0 a x 2 + b x + c = 0. Since the solutions of the equations give the x-intercepts of the graphs, the number of x-intercepts is the same as the number of solutions. The graphs below show examples of parabolas for these three cases. The solutions of the quadratic equation are the x x values of the x-intercepts.Įarlier, we saw that quadratic equations have 2, 1, or 0 solutions. ![]()
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