﻿Hi, I'm Miss Davies. In this lesson, we're going to be solving quadratic graphs. A quadratic graph is written in the form y is equal to axe squared add bx add c. When we solve a quadratic, this should be equal to zero. The solution or solutions also known as the roots are the points that cross the x-axis. The x-axis is also known as the line y is equal to zero. We can see on our graph that the function crosses the X-axis in two different places. If asked to solve the graph axe squared add bx add c is equal to 10. We can simply plot the graph of y is equal to 10. And read the x-coordinate of the points of intersection. If we look at this graph, we can draw on the line of y is equal to 10. These have two points of intersection. The solution to this equation would be x is equal to two, and x is equal to negative 3.5. We're going to use the graph that is given to find estimates for the solutions of these three equations. For the first example, five x squared subtract three x subtract one is equal to zero. This means we are looking along the x-axis. Or the line y is equal to zero. This gives the x-coordinate of approximately negative 0.25 and 0.85. These are the two estimates for the solutions of x. With the next example, our function is equal to negative one. We're going to draw on the graph of x is equal to negative one. This gives us two points of intersection. The first has an x-coordinate of zero. The second has an approximate x value of 0.6. With the third example, we're going to draw the graph of y is equal to 2.5. Again, this has two points of intersection. The approximate values for x are negative 0.6 and 1.2. Here's some questions for you to try. Pause the video to complete your task and resume once you've finished. Here are the answers. Each horizontal line intersects the curve at two points, giving two solutions for x. Your answers might be slightly different. Note 0.2 higher or lower than these answers will be fine. This time we're going to use the graph to find estimates of x, when the function is equal to an expression containing x. For the first example, we're going to draw the line y is equal to x. This has two points of intersection. The x-coordinates of these two points are approximately negative 0.2 and one. For the second example, we're going to draw the line y is equal to one subtract x. Again, this has two points of intersection. The x-coordinate of these two points are approximately negative 0.45 and 0.85. For our final example, we're going to draw the line of y is equal to two x add 1.8. This has two points of intersection. The x-coordinates of these points are approximately negative 0.2 and 1.4. Here's some questions for you to try. Pause the video to complete your task and resume once you've finished. Here are the answers. Again, there are two points of intersection for each straight line, giving two solutions. Here are some questions for you to try. Pause the video to complete your task and resume once you've finished. Here were the answers. Part C doesn't have any solutions as the two lines don't intersect at any point. That's all for this lesson. Thanks for watching.

In this lessons we will learn how to use graphs to find solutions to equations where one is quadratic and one is linear.

Maths

Y11 Maths (Core)

Key Stage 4

Year 11

Miss

Solve quadratic graphs = 0, = a and = ax + b

Y10 Maths (Core)

Year 10

Y10 Maths (Higher)

Quadratic Graphs 2 (a>1)

Algebra (A)

THEME

UNIT

Draw quadratic graphs (a > 1)

Draw quadratic graphs (negative x squared)

Solving quadratic equations, given a different quadratic, using a sketch

Y11 Maths (Higher)

Revise - Linear and Quadratic Graphs

Find the gradient of a line

Find the equation of a straight line using y=mx+c

Find the intercept and gradient from a line given in any form

Using gradient to solve problems with parallel lines

Plot simple quadratic equations

Plot other quadratic equations

Solving Quadratic Equations Graphically

Identify and interpret roots, intercepts and turning points of quadratic graphs

Lesson overview: Solve quadratic graphs = 0, = a and = ax + b

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4 lessons in Quadratic Graphs 2 (a>1):

12 lessons in Revise - Linear and Quadratic Graphs: