SOME Be able to use quadratic graphs to

SOME: Be able to use quadratic graphs to solve practical problems Lesson Objective: To be able to draw a quadratic graph, given its equation. (Grade Level 5)

What is a quadratic graph? A quadratic graph has an equation that involves x². Once drawn, the graph makes a smooth curve. All of the following are quadratic equations and each produce a quadratic graph: y = x² + 5 y = x² - 3 x y = x² + 5 x + 6 y = x² + 2 x - 5 y = x² - 6 x + 18

Draw the graph of y = x² for -3 ≤ x ≤ 3. First make a table, as shown below: -3 -2 -1 0 1 2 3 9 4 1 0 1 4 9 Now draw axes, with -3 ≤ x ≤ 3 and 0 ≤ y ≤ 9, plot the points and join them to make a smooth curve. This is the graph of y = x² This type of graph is often referred to as a parabola.

Draw the graph of y = x² + 2 x – 3 for -4 ≤ x ≤ 2. -4 -3 -2 -1 0 1 2 1 4 16 9 4 1 0 -8 -6 -4 -1 0 2 4 -3 -3 -3 5 -3 0 -3 -4 -3 0 5 Generally, you do not need to draw a table with as many values as this, but if it helps you with your calculations, by all means do it.

Find the values of x that give a y-value of 1. Start at 1 on the y-axis and read off the two x-values that correspond to a y-value of 1. Make sure you draw arrows to show your working as even though you may get the answer wrong you may get a working mark. x = -3. 2 and x = 1. 2 When you are given the proper graph paper shortly, your answers will be more accurate.

What do you notice about the shapes of the graphs that you have drawn? What do you notice about your x and y-values in your tables?

Outcome: Grade: Next Steps: At the end of today’s lesson, I can now… and have worked at a Grade… To improve, I need to be able to… use quadratic graphs to solve practical problems 4/5. draw a cubic graph. 4/5. use quadratic graphs to solve practical problems. 5.