Quadratic Inequalities

Question 1

what can replace the equals sign in an equation

Answer 1

An inequality

Question 2

What does placing an inequality do to an equation

Answer 2

It makes it so there is no longer a single number that solves the equation but rather a range of solutions

Question 3

What steps do we need to follow when sketching a graph using inequalities

Answer 3

1. Replace the inequality with an equals sign and find the solution(s) to the quadratic equation.
2. Sketch a graph of the function. All that is needed for this sketch is a horizontal line (to represent thex- axis), the solution(s) found in Step 1 (marked as points), and the parabola drawn roughly, either as a ‘smile’ or a ‘frown’ (depending on whethera is positive or negative in the equation written in the formax^2+bx+c=0
3. Read off (and write down as an inequality or two inequalities, as appropriate) the relevantx-values where the graph is either positive or negative (whatever is required by the inequality), using thex-axis as a number line.

Question 4

What happens to the inequality symbol when we divide

Answer 4

It flips ( changes direction )

Question 5

How do we solve quadratic inequalities

Answer 5

1. get a 0 on the one side of the inequality (put everything onto one side)
2. now work out the inequality like a Trinomial
3. now make both sums in the bracket equal 0 (or)
4. now solve for x for two sums
5. once we have both values for x we must draw a number line
6. on the number line draw two points for our two values and draw in the positive and negative infinity
7. if the solution includes the values then draw a closed circle (if it doesn’t include the point then we add an open circle