iGCSE (2021 Edition)

# 4.06 Discriminant and parabolas

## Interactive practice questions

Consider a parabola of the form $y=ax^2+bx+c$y=ax2+bx+c, where $a>0$a>0

a

Which of the following statements is true?

The vertex of the parabola is a maximum point.

A

The vertex of the parabola is a minimum point.

B

The vertex of the parabola is a maximum point.

A

The vertex of the parabola is a minimum point.

B
b

Each parabola below has an equation of the form $y=ax^2+bx+c$y=ax2+bx+c.

Select all the graphs for which $a>0$a>0

A

B

C

D

A

B

C

D
Easy
Less than a minute

Consider the equation $4x^2+4x-6=0$4x2+4x6=0.

Consider the equation $4x^2-4x+1=0$4x24x+1=0.

To find the $x$x-intercepts of a particular parabola, $ax^2+bx+c=0$ax2+bx+c=0, Katrina used the quadratic formula and found that $b^2-4ac=-5$b24ac=5. How many $x$x-intercepts does the parabola have?

### Outcomes

#### 0606C2.1

Find the maximum or minimum value of the quadratic function f : x ↦ ax^2 + bx + c by any method.

#### 0606C2.2

Use the maximum or minimum value of f(x) to sketch the graph or determine the range for a given domain.

#### 0606C2.3

Know the conditions for f(x) = 0 to have two real roots, two equal roots, no real roots. Know the related conditions for a given line to intersect a given curve, be a tangent to a given curve, not intersect a given curve.