How do you find where the graph crosses the x-axis?

Solve ax^2+bx+c=0 by factorising or by the formula.

Equation of the line of symmetry?

x=-\frac{b}{2a}, halfway between the roots

How do you find the y-coordinate of the vertex?

Substitute the line-of-symmetry value into f(x).

Vertex of y=x^2-6x+5?

(3,-4), a minimum, since y=(x-3)^2-4

What are the four things to show on a quadratic sketch?

Shape, y-intercept, roots, vertex.

How many times can a quadratic graph meet the x-axis?

Twice, once (touching, repeated root) or not at all.

Two points on a parabola at the same height: how are they related to the line of symmetry?

They are equal distances either side of it.

Quadratic functions and their graphsEdexcel International A Level Maths: Flashcards

Card 1 of 120 of 12 known

Question

What is the shape of $y=ax^2+bx+c$ when $a>0$ and when $a<0$?

Tap or press Space to reveal

Tap card or press Space to flip

See all 12 cards

What is the shape of $y=ax^2+bx+c$ when $a>0$ and when $a<0$ ?: $a>0$ : $\cup$ -shaped with a minimum. $a<0$ : $\cap$ -shaped with a maximum.
Where does $y=ax^2+bx+c$ cross the $y$ -axis?: At $(0,c)$
How do you find where the graph crosses the $x$ -axis?: Solve $ax^2+bx+c=0$ by factorising or by the formula.
Factorised form of a quadratic with roots $p$ and $q$ ?: $a(x-p)(x-q)$
Equation of the line of symmetry?: $x=-\frac{b}{2a}$ , halfway between the roots
How do you find the $y$ -coordinate of the vertex?: Substitute the line-of-symmetry value into $f(x)$ .
Where is the vertex of $a(x+p)^2+q$ ?: At $(-p,q)$
Vertex of $y=x^2-6x+5$ ?: $(3,-4)$ , a minimum, since $y=(x-3)^2-4$
What are the four things to show on a quadratic sketch?: Shape, $y$ -intercept, roots, vertex.
How many times can a quadratic graph meet the $x$ -axis?: Twice, once (touching, repeated root) or not at all.
Range of $f(x)=(x-3)^2-4$ ?: $f(x)\ge-4$
Two points on a parabola at the same height: how are they related to the line of symmetry?: They are equal distances either side of it.

Exam questions on Quadratic functions and their graphs

The quadratic function $f(x)=x^2-6x+5$ .
Find the coordinates of the minimum point of the graph of $y=f(x)$ .2 marks
A curve $C$ has equation $y=-2x^2+8x-3$ .
The line $y=-3$ meets $C$ at two points. Find the $x$ -coordinates of these points.2 marks
A quadratic function is $f(x)=2x^2+px+q$ , where $p$ and $q$ are constants. The graph of $y=f(x)$ crosses the $x$ -axis at $x=-1$ and $x=\frac52$ .
Find the values of $p$ and $q$ .3 marks

See the full worksheet

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).