(11 Nov 21) Linear/quadratic knowledge and solving quadratic equations

LINEAR versus QUADRATIC graph plotting

This will take some time to play around with to get the right answers, but will give you good insight into graphing and how to change how a graph looks through the equation

Use the DESMOS tool to work these out (https://www.desmos.com/calculator)

1. What is a possible the equation for a LINEAR graph that is very steep, goes downhill, and passes through the x axis at 6

2. What is a possible equation for a LINEAR graph that is only a little bit uphill, and passes through the y axis at -3

3. What is a possible equation for a LINEAR graph that is uphill and passes through the x axis at 6 and the y axis at -1

4. What is a possible equation for a LINEAR graph that is downhill, and passes through the x axis at -10

Use the DESMOS tool to work these out (https://www.desmos.com/calculator)

1. What is a possible equation for a QUADRATIC graph that is that shape of a happy face and passes through the x axis at two different points

2. What is a possible equation for a QUADRATIC graph that is that shape of a sad face and passes through the x axis at two different points

3. What is a possible equation for a QUADRATIC graph that is that shape of a happy face and passes through the x axis at only one point

4. What is a possible equation for a QUADRATIC graph that is that shape of a sad face and doesn't pass through the x axis

How to work with quadratic relationships and graphs

1. What step can you take to find the y intercept of a quadratic equation?

2. What steps do you take to find the x intercepts of a quadratic equation?

3. What step can you take to find the turning point of a quadratic equation?

Solve a quadratic equation

To solve a quadratic equation means to find out the value of x that can be true

1. Factorise

2. For the equation to be true, one of the factors (expressions in the brackets) must be true. Find the values of x that make the equation true.

Solve a quadratic equation by factorising

Solve these quadratics by factorising and finding the values of x that make the equation true.

Find the y intercept

Find the y intercept of these LINEAR equations by letting x = 0. Write your answers as coordinates e.g. (0, -2)

Find the y intercept of these QUADRATIC equations by letting x = 0. Write your answers as coordinates e.g. (0, -2)

Solve (find x int), find y intercept and find the turning point

For the 4 quadratic relations below, find:

a. the x intercepts (factorise and solve)

b. find the y intercept by letting x = 0

c. find the turning point (in the middle of the x intercepts)