Chapter 9, Lesson 2: Solving Quadratic Equations by Graphing. About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features NFL Sunday Ticket Press Copyright. Use the Quadratic Formula to solve each equation. Graphing Technology Personal Tutors Other Calculator Keystrokes Meet the Authors About the Cover.ĩ-8The Quadratic Formula Warm Up Evaluate for x = –2, y = 3, and z = –1. by completing the square, ( x + 5) 2 16 so x ± 4 - 5 (from above) by the quadratic formula. You can see hints of this when you solve quadratics. a, b and c are left as letters, to be as general as possible. Solve each quadratic equation by factoring. The quadratic formula actually comes from completing the square to solve ax2 + bx + c 0.x= 80 x = 10 x = 20ĩ-7Completing the Square Warm Up Part I Simplify. vertex:(–2, –1) zeros:–3, –1ĩ-5Solving Quadratic Equations by Factoring Identify the vertex and zeros of the function above. y = 2x2 +2x – 8 x = 0 x = 1 (0, 2) (–2, 1)ĩ-4Solving Quadratic Equations by Graphing Warm Up 1. y = x2 + 2x + 3, when x = –1 –2 –12 2ĩ-3Graphing Quadratic Functions Warm Up Find the axis of symmetry. Example 1, i wrote x-1 was a solution, but x1 is the actual solution0:00 - Intro0:54 - Ex. Parabolas are symmetric, so we can find the x -coordinate of the vertex by averaging the x -intercepts. To draw the rest of the parabola, it would help to find the vertex. We’re not big fans of you memorizing formulas, but this one is useful (and we think you should learn how to derive it as well as use it, but that’s for the second video). y = 3x + 6 Evaluate each quadratic function for the given input values. So our solutions are x 3 and x 2, which means the points ( 2, 0) and ( 3, 0) are where the parabola intersects the x -axis. The quadratic formula helps you solve quadratic equations, and is probably one of the top five formulas in math. Generate ordered pairs for the function y = x2 + 2 for x-values –2, –1, 0, 1, and 2.ĩ-2Characteristics of Quadratic Functions Warm Up Find the x-intercept of each linear function. X –2 –1 0 1 2 y 6 3 2 3 6 9-1 Quadratic Equations and Functions We can see the graph of \(g\) is the graph of \(f(x)=x^2\) shifted to the left 2 and down 3, giving a formula in the form \(g(x)=a(x+2)^2–3\).Warm Ups Preview 9-1 Quadratic Equations and Functions 9-2 Characteristics of Quadratic Functions 9-3 Graphing Quadratic Functions 9-4 Solving Quadratic Equations by Graphing 9-5 Solving Quadratic Equations by Factoring 9-6 Solving Quadratic Equations by Using Square Roots 9-7 Completing the Square 9-8 The Quadratic Formula 9-9 The Discriminant A quadratic function is messier than a straight line it graphs as a wiggly parabola. Algebra would be the only sure solution method. Then, add or subtract the two equations to eliminate one of the variables. If the linear equation were something like y 47x 103, clearly well have great difficulty in guessing the solution from the graph.We might guess that the x-intercept is near x 2 but, while close, this wont be quite right. \): Graph of a parabola with its vertex at \((-2, -3)\). To solve a system of equations by elimination, write the system of equations in standard form: ax + by c, and multiply one or both of the equations by a constant so that the coefficients of one of the variables are opposite.
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