Week 12 A Finding Solutions from Graphs

Week 12 A Finding Solutions from Graphs

Finding Solutions from Graphs

Objectives

• Bronze: I can: Draw Quadratic and cubic graphs

• Silver: I can: Find a point where two lines meet.

• Gold: I can: Find solutions to graphs.

Drawing Graphs of quadratic and cubic equations

Sketching a graph means to draw the graph, we can do this in the same way as we would draw a linear equation. We would:

Substitute values of x into a table of values for that equation.

Plot the points.

Join the points using a soft curve.

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Drawing Graphs of quadratic equations

• Sketch the graph of the quadratic equation y = x² – 3x - 2

Graphical Solution of Equations

• Use the graph of y = x² + 2x -3 to solve x² + 2x - 3 = 0

• Remember: the x axis has equation y = 0

• Simply read off the x values at the points of intersection.

• Solutions: x = 1 and -3

Graphical Solution of Equations 

• Use the graph of y = x² + 2x -3 to estimate solutions x² + 2x - 3 = 4

• Draw the line y = 4

• Read off the x values at the points of intersection.

• Solutions: 

  x = 1.8 and -3.8

Graphical Solution of Equations 

• Use the graph of y = x² + 2x -3 to solve x² + 2x -3 = x - 1

• Draw the graph of y = x - 1

• Simply read off the x values at the points of intersection of both graphs.

• Solutions: x = 1 and -2

Multiple Choice

How many solutions are there when y = 0?

• 1 Solution

• 2 Solutions

• No Solution

• Empty set. Does not equal to zero.

How many solutions are there when y = 0?

There are two solutions. These are highlighted in yellow.

The x-axis is where y = 0, so the solutions are where the graph crosses the x-axis.

Multiple Select

Select all that apply.

• 1 Solution

• 2 Solutions

• No Solutions

• Empty Set. Does Not Equal Zero.

• Crosses the x-axis.

Select all that apply

• There are two solutions as the graph crosses the x-axis in two places.

• The graph also crosses the y-axis at y = -2

Multiple Select

Find the solutions of this quadratic graph when y = 0. Select all that apply.

• 1.2

• -3

• 4.8

• 6

• 3

Find the solutions of this quadratic graph when y = 0.

• The graph crosses the x-axis (y = 0) at x = 1.2 and 4.8

Multiple Select

Find the solutions of this quadratic graph when y = 0. Select all that apply.

• -10

• -5

• -3

• 5

• 3

Find the solutions of this quadratic graph when y = 0.

• Even though this graph is upside down (because it has a negative x²) we still look for where it crosses the x-axis (y = 0)'

• It crosses at x = -5 and -3, so these are it's solutions.

Multiple Choice

Find the solutions of this quadratic graph when y = 0. Select all that apply.

• -2

• -4

• 0

• 4

• 2

Find the solutions of this quadratic graph when y = 0

• As this graph only touches the x-axis (y = 0) in one spot, it only has one solution.

• The graph touches y = 0 at x = -2, so this is the solution.

Multiple Select

Find the solutions of this quadratic graph when y = 3. Select all that apply.

• -1

• 4

• -3

• 2

• -5

Find the solutions of this quadratic graph when y = 3

• For this question, we are looking for a solution at y = 3, so we must draw the graph on y = 3.

• The graph crosses y = 3 at the points x = -3 and x = -1, so this is the solution when y = 3.

Multiple Select

Find the solutions of this quadratic graph when y = -5. Select all that apply.

• -2

• -9

• 0

• 2

• 4

Find the solutions of this quadratic graph when y = -5

• For this question, we are looking for a solution at y = -5, so we must draw the graph on y = -5.

• The graph crosses y = -5 at the points x = -2 and x = 2, so this is the solution when y = -5

Exit Ticket

Complete the Century task set for this week. You must do this to get your mark.