Solving Quadratic Equations with Graphs Slideshow 31, Mathematics Mr. Richard Sasaki, Room 307

Objectives Recall how to draw graphs with linear equations Recall how to draw graphs with linear equations Be able to solve simultaneous equations graphically with both linear and quadratic lines Be able to solve simultaneous equations graphically with both linear and quadratic lines Be able to do this with real world examples Be able to do this with real world examples

Linear Graphs First let’s have a review on how to draw linear graphs. Linear graphs are in the form. They are straight lines and much easier to draw than quadratic graphs. Example

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Solving Simultaneous Equations Graphically If we have a pair of simultaneous equations, do you remember how to solve them graphically? Example First draw both of the lines. The solution is simply the intersection. So we get.

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Where’s the vertex? Quadratic Simultaneous Equations Let’s solve some simultaneous equations with quadratics like in Grade 8, but with graphs. Example 1 1 The parabola allows for up to two intersections: That’s our two pairs of solutions!

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Real World Equations and Graphs Now we will look at some non-simultaneous real world problems. Example

Real World Equations and Graphs Now we need to place that vertex on the grid and draw the line. How fast was the car travelling when the brakes were applied? After how many seconds did the car reach its maximum speed? What was it?

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Graphing Real World Simultaneous Equations Usually problems with simultaneous equations discuss their intersection. This could imply when a person catches up with another, an object lands on a slope or another meaning. Example We should write the dogs’ statement in terms of how far it has travelled.

Graphing Real World Simultaneous Equations

Let’s draw the lines. We know the boy catches up with his dog at the intersection, so it takes…

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