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![]() 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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