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Year 10
Higher

Key features of a quadratic graph

I can identify the key features of a quadratic graph.

icon-background-square
New
New
Year 10
Higher

Key features of a quadratic graph

I can identify the key features of a quadratic graph.

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Lesson details

Key learning points

  1. A quadratic graph is a parabola.
  2. The roots of a quadratic graph are where the graph intersects with the x-axis.
  3. The turning point is the maximum or minimum point of the graph.
  4. The coordinates of the turning point can be found by completing the square.

Keywords

  • Roots - When drawing the graph of an equation, the roots of the equation are where its graph intercepts the x-axis (where y = 0).

  • Turning point - The turning point of a graph is a point on the curve where, as x increases, the y values change from decreasing to increasing or vice versa.

Common misconception

Parabolas are 'upwards' or 'downwards'.

Encourage use of language such as \"The turning point of this parabola is a maximum/minimum value\" and \"As the absolute values of $$x$$ increase, the $$y$$ values decrease/increase\".


To help you plan your year 10 maths lesson on: Key features of a quadratic graph, download all teaching resources for free and adapt to suit your pupils' needs...

Model good technical language and get pupils to repeat it to you. This encourages use of the correct mathematical language.
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Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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6 Questions

Q1.
What shape is the graph of the equation $$y = 6x^2-3x+9$$?
A linear graph
Correct answer: A parabola
An upward curve
A vertical line
Q2.
What is the $$y$$-intercept of this linear graph?
An image in a quiz
(2, 0)
Correct answer: (0, -4)
$$x$$ = 0
$$y$$ = -4
Q3.
Which of these are key features of the graph of the equation $$3x+y=6$$?
An image in a quiz
Gradient of 3
Correct answer: $$x$$-intercept at (2, 0)
Correct answer: Gradient of -3
Correct answer: Linear graph
Correct answer: $$y$$-intercept at (0 ,6)
Q4.
Factorise $$x^2-8x+7$$.
$$(x-8)(x+7)$$
$$(x-7)(x+1)$$
Correct answer: $$(x-7)(x-1)$$
$$(x+4)(x+3)$$
$$(x+7)(x+1)$$
Q5.
Factorise $$x^2-8x+16$$.
$$(x+4)(x-4)$$
$$(x+4)^2$$
Correct answer: $$(x-4)^2$$
$$(x-8)(x+16)$$
Q6.
Expand and simplify $$(x+5)^2-10$$
$$x^2+15$$
$$x^2+5x+15$$
$$x^2+25x+15$$
Correct answer: $$x^2+10x+15$$
$$x^2+10x+25$$

6 Questions

Q1.
$$x=-2$$ and $$x=3$$ are __________ of the equation shown in this graph.
An image in a quiz
intercepts
intersects
Correct answer: roots
Correct answer: solutions
Q2.
(3, 1) is the __________ of this quadratic graph.
An image in a quiz
bottom
end
lowest solution
Correct answer: minimum point
Correct answer: turning point
Q3.
What are the roots of this equation?
An image in a quiz
(2, 0)
Correct answer: $$x$$ = 2
$$x$$ = 3
Correct answer: $$x$$ = 4
$$x$$ = 8
Q4.
What is the turning point of this graph?
An image in a quiz
$$x$$ = 2
$$x$$ = 3
(0, 8)
(2, 0)
Correct answer: (3, -1)
Q5.
Factorise $$y=x^2-4x-12$$ to find the roots of the equation.
$$(x-3)(x-4)$$, therefore roots at $$x=3$$ and $$x=4$$
$$(x+6)(x-2)$$, therefore roots at $$x=-6$$ and $$x=2$$
Correct answer: $$(x-6)(x+2)$$, therefore roots at $$x=6$$ and $$x=-2$$
$$(x+3)(x+4)$$, therefore roots at $$x=-3$$ and $$x=-4$$
Q6.
The quadratic equation $$y=x^2+14x+49$$ has __________.
no roots
one root
Correct answer: one repeated root
two roots