Key features of a quadratic graph | Maths | Quizalize & Oak National Academy

Starter quiz

What shape is the graph of the equation $y = 6x^2-3x+9$ ?

A linear graph

A parabola ✓

An upward curve

A vertical line
What is the $y$ -intercept of this linear graph?

(2, 0)

(0, -4) ✓

$x$ = 0

$y$ = -4
Which of these are key features of the graph of the equation $3x+y=6$ ?

Gradient of 3

$x$ -intercept at (2, 0) ✓

Gradient of -3 ✓

Linear graph ✓

$y$ -intercept at (0 ,6) ✓
Factorise $x^2-8x+7$ .

$(x-8)(x+7)$

$(x-7)(x+1)$

$(x-7)(x-1)$ ✓

$(x+4)(x+3)$

$(x+7)(x+1)$
Factorise $x^2-8x+16$ .

$(x+4)(x-4)$

$(x+4)^2$

$(x-4)^2$ ✓

$(x-8)(x+16)$
Expand and simplify $(x+5)^2-10$

$x^2+15$

$x^2+5x+15$

$x^2+25x+15$

$x^2+10x+15$ ✓

$x^2+10x+25$

Exit quiz

$x=-2$ and $x=3$ are __________ of the equation shown in this graph.

intercepts

intersects

roots ✓

solutions ✓
(3, 1) is the __________ of this quadratic graph.

bottom

end

lowest solution

minimum point ✓

turning point ✓
What are the roots of this equation?

(2, 0)

$x$ = 2 ✓

$x$ = 3

$x$ = 4 ✓

$x$ = 8
What is the turning point of this graph?

$x$ = 2

$x$ = 3

(0, 8)

(2, 0)

(3, -1) ✓
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 $x=2$

$(x-6)(x+2)$ , therefore roots at $x=6$ and $x=-2$ ✓

$(x+3)(x+4)$ , therefore roots at $x=-3$ and $x=-4$
The quadratic equation $y=x^2+14x+49$ has __________.

no roots

one root

one repeated root ✓

two roots

Worksheet

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Lesson Details

Key learning points

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

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\".

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.