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Published byKristina Hensley Modified over 5 years ago

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Factor and Solve: 1.x² - 6x – 27 = 0 2.4x² - 1 = 0 Convert to Vertex Format by Completing the Square (hint: kids at the store) 3. Y = 3x² - 12x + 20

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I can write a quadratic equation given solutions from the graph

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Identify the 3 forms of a quadratic equation: Standard Formatax² + bx + c *** c is where the graph crosses the y axis *** Vertex Formaty = a(x – h)² + k *** gives the vertex (h, k) *** Intercept Formaty = a(x – p)(x – q) *** gives the roots, zeros or solutions of the graph ***

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Write a quadratic equation in standard form that has the given solutions and passes through the given point. A quadratic equation has roots of {-1, -3} and passes though (-4, 3). Which quadratic format is best to use given the roots of the graph? INTERCEPT FORMy=a(x – p)(x – q)

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y = a (x - p)(x - q) y = a (x + 1)(x + 3 )Substitute -1 for p and -3 for q A quadratic equation has roots of {-1, -3} and passes though (-4, 3). Use the other given point (-4, 3) to find A Step 1: Step 2: 3 = a (-4+1)(-4 + 3) Replace y With 3 Replace x With -4

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A quadratic equation has roots of {-1, -3} and passes though (-4, 3). 3 = a(-3)(-1)Simplify 3 = 3aSimplify 1 = aSolve for a 3 = a (-4+1)(-4 + 3 ) Step 3: Step 4: The quadratic equation for the parabola in intercept form y = 1(x + 1)(x + 3)

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To find the equation for the parabola in standard form you will need to FOIL. 1(x² + 3x + 1x -4)FOIL 1(x² + 4x - 4)Simplify x² + 4x - 4Distribute

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Your Turn Write an quadratic equation in standard format: ax² + bx + c = 0 that has the given solutions and passes through the given point. Example: A quadratic equation has roots of {-1, 4} and passes though (3, 2).

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