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### Transcript

• 1. Solving & Graphing the Quadratic Equation Created by Yvette Lee Source: mathisfun, purplemath, www.chaoticgolf.com/pptlessons/graphquadraticfcns2.ppt
• 2. What is quadratic equation? The name Quadratic comes from "quad" meaning square, because the variable gets squared (like x2)
• 3. Quadratic Functions The graph of a quadratic function is a parabola. A parabola graph has an open U-shape NOTE! Make sure the parabola doesn’t stop at the end of the curve. It is continuous for all x- values. y x
• 4. y x Line of Symmetry Line of Symmetry Parabolas have a symmetric property to them. If we drew a line down the middle of the parabola, we could fold the parabola in half. We call this line the line of symmetry. The line of symmetry ALWAYS passes through the middle point horizontally. Or, if we graphed one side of the parabola, we could “fold” (or REFLECT) it over, the line of symmetry to graph the other side.
• 5. What is the Standard Form of a Quadratic Equation? * a, b and c are known values. a can't be 0. * "x" is the variable or unknown (you don't know it yet).
• 6. Let’s find a, b, and c in the examples below. In this one a=2, b=5 and c=3 Where is a? In fact a=1, as we don't usually write "1x2" b = -3 And where is c? Well, c=0, so is not shown. Oops! This one is not a quadratic equation, because because it is missing x2 (in other words a=0, and that means it can't be quadratic)
• 7. But sometimes a quadratic equation doesn't look like that! For example:
• 8. How do we find solutions to the quadratic equations? What is solutions? The "solutions" to the Quadratic Equation are where it is equal to zero. There are usually 2 solutions (as shown in the graph above). They are also called "roots", or sometimes "zeros"
• 9. How to graph the quadratic equation 1. Find the Standard form of the quadratic equation. 2. Find the solutions(zeroes, roots) of the equation. They are x-values on the x-axis 3. Find y-intercept (c value in the standard form, or the term without variables) Standard form x-value (roots) y-intercept
• 10. A trick when you see (x-a)(x-b)=0 Solve (x + 1)(x – 3) = 0 This is a quadratic, and I'm supposed to solve it. I could multiply the left-hand side, simplify to find the coefficients, plug them into the Quadratic Formula, and chug away to the answer. But why would I? I mean, for heaven's sake, this is factorable, and they've already factored it and set it equal to zero for me. While the Quadratic Formula would give me the correct answer, why bother with it? Instead, I'll just solve the factors: (x + 1)(x – 3) = 0 x + 1 = 0 or x – 3 = 0 x = –1 or x = 3 The solution is x = –1, 3 * If you want to distribute the equation and use the formula to find the roots, it works too. This is just a easier and quicker way to solve it.
• 11. Solve and graph x2+5x=-6 1. Is it the standard form? No! I add 6 in each side to make the right side to zero: x2+5x+6=0 2. What are the roots/zeroes/solutions? a=1, b=5, c=6 Plug the numbers in the calculator or use factoring (x+2)(x+3)=0 The solution is x=2, or 3 3. Find y-intercept. C=6, so y-intercept is 6. Time to draw the graph. Plot the roots and the y-intercept and make a symmetrical U shape
• 12. Solve and graph x2+4x=-4 1. Is it the standard form? No! I add 4 in each side to make the right side to zero: x2+4x+4=0 2. What are the roots/zeroes/solutions? a=1, b=4, c=4 Plug the numbers in the calculator or use factoring (x+2)(x+2)=0 The solution is x=2, or 2 3. Find y-intercept. C=4, so y-intercept is 4. Time to draw the graph. Plot the roots and the y-intercept and make a symmetrical U shape