Solving quadratic equations by graphing. X Y I x² - 2x = 3 You have to rewrite the equation to find the vertex before you can graph this function Use.

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Presentation transcript:

Solving quadratic equations by graphing

X Y I x² - 2x = 3 You have to rewrite the equation to find the vertex before you can graph this function Use the formula -b 2a a = 1 b = -2 c = ∙ The x coordinate of the vertex is at 1 Substitute to find the y value The vertex is at (1, -4) The solutions are found where the graph crosses the x-axis ( x intercepts) x² - 2x – 3 = 0 One solution is At (-1, 0) One solution is At (3, 0)

X Y I 2x = x² + 1 You have to rewrite the equation to find the vertex before you can graph this function Use the formula -b 2a a = -1 b = 2 c = ∙-1 -2 The x coordinate of the vertex is at 1 Substitute to find the y value The vertex is at (1, 0) The solutions are found where the graph crosses the x-axis ( x intercepts) -x² + 2x – 1 = 0 This graph only has one solution at (1, 0)

X Y I x² + 7 = 4x You have to rewrite the equation to find the vertex before you can graph this function Use the formula -b 2a a = 1 b = -4 c = ∙ The x coordinate of the vertex is at 2 Substitute to find the y value The vertex is at (2, 3) The solutions are found where the graph crosses the x-axis ( x intercepts) x² - 4x + 7 = 0 This equation has no real solution because the graph does NOT touch the x-axis at all

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X Y I x² - 2x = 3 You have to rewrite the equation to find the vertex before you can graph this function Use the formula -b 2a a = b = c = - 2 ∙ The x coordinate of the vertex is at Substitute to find the y value The vertex is at (, ) The solutions are found where the graph crosses the x-axis ( x intercepts) = 0 One solution is At (, ) One solution is At (, )

X Y I 2x = x² + 1 You have to rewrite the equation to find the vertex before you can graph this function Use the formula -b 2a a = b = c = - 2 ∙ The x coordinate of the vertex is at Substitute to find the y value The vertex is at (, ) The solutions are found where the graph crosses the x-axis ( x intercepts) = 0 This graph only has one solution at (, )

X Y I x² + 7 = 4x You have to rewrite the equation to find the vertex before you can graph this function Use the formula -b 2a a = b = c = - 2 ∙ The x coordinate of the vertex is at Substitute to find the y value The vertex is at (, ) The solutions are found where the graph crosses the x-axis ( x intercepts) = 0