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Solve Quadratic Equations by Graphing (10.3) Definition: A Quadratic Equation is an equation that can be written in the standard form: ax2 + bx + c = 0 Write the equation in standard form. Ex. x2 – 2x = 3 Ex. x2 + 5x = -7 Ex. x2 + 7 = 4x Ex. x2 = -2x + 9 Remember that a Solution to any equation is the number or numbers that make the equation true. So the Solution for a Quadratic Equation value or values of x that will make the quadratic function equal 0. Determine whether the given value is a solution of the equation. Ex. x2 + 3x – 10= 0; 5 Ex. x2 – 5x – 6 = 0; 6 Ex. x2 – 4x – 5 = 0; -5 Ex. x2 – 6x – 16 = 0; -2 We learned that we can solve a quadratic equation by Factoring last chapter. x2 + 6x + 5 = 0 Solutions: x = ______ and x = ______ Now look at the graph of y = x2 + 6x + 5 Notice that the two solutions that we found by factoring x = ________ and x = ______ are the points on the ___________ where the parabola intersects it. 1 Quadratic Equations can have a different number of solutions depending on where the parabola is on the coordinate system. _____ Solution(s) ______ Solution(s) _______ Solution(s) _____ point(s) of intersection _____ point(s) of intersection _____ point(s) of intersection Use the graph to find the solution(s) of the given equation. Ex. x2 – 5x + 4 = 0 Ex. x2 – 6x + 9 = 0 Ex. x2 + 5 = 0 Solution ____________ Solution ____________ Solution ____________ Ex. x2 – 6x – 16 = 0 Ex. -3x2 + 6 = 0 Ex. x2 + 10x + 25 = 0 Solution ____________ Solution ____________ Solution ____________ 2