Graphs of Functions (OCR GCSE Maths: Foundation): Exam Questions

Here is the graph of  $y=x^2-5x+3$

Use your graph to find estimates of the solutions to  $0=x^2-5x+3$ 

Complete this table for $y=x^2-4$.

Draw the graph of $y=x^2-4$ for values of $x$ from $-3$ to $3$.

Use the graph to solve the equation $x^2-4=1$.

Give your answers to $1$ decimal place.

Complete the table of values for $y=1+5x-x^2$

On the grid, draw the graph of $y=1+5x-x^2$ for $-1⩽x⩽5$.

The line $L$ is shown on the grid.
Find the equation of the line in the form $y=mx+c$.

$y$ = .............................................. 

i) Complete the table of values for $y=x^2+2x+4$.

[2]

ii) On the grid opposite, draw the graph of $y=x^2+2x+4$ for $–2⩽x⩽3.$

[4]

For $–2⩽x⩽3,$ write down the $x$-coordinate of the point of intersection of the line $L$ with the curve
$y=x^2+2x+4.$

$x=$...............................

Complete the table of values for $y=5+2x-x^2$.

On the grid, draw the graph of $y=5+2x-x^2$ for $-2⩽x⩽4$.

i) On the grid, draw the line of symmetry.

[1]

ii) Write down the equation of the line of symmetry.

[1]

i) On the grid, draw a line from $(-1,2)\mathrm{to}(1,6).$

[1]

ii) Find the equation of this line in the form $y=mx+c.$

$y=$ ............................ [3]

i) Complete the table of values for $y=x\left(3-x\right)$.

[3]

ii) On the grid, draw the graph of $y=x\left(3-x\right)$ for $-4⩽x⩽4.$

[4]

iii) Write down the co-ordinates of the highest point of the graph for $-4⩽x⩽4.$

[1]

i) Complete the table of values for $y=x^2-x-5.$

[3]

ii) On the grid, draw the graph of $y=x^2-x-5\mathrm{for}-3⩽x\mathit{⩽}4.$

[4]

iii) Write down the co-ordinates of the lowest point on the graph.

[1]

iv)

a) On the grid, draw the line of symmetry of the graph.

[1]

b) Write down the equation of this line.

[1]

The diagram shows the graph of $y=x^2+8x-9$.

The graph crosses the $x$-axis at $x=-9$ and $x=1$.

Write down the coordinates of the point where the graph crosses the $y$-axis.

Write down the equation of the line of symmetry of the graph.

Here is a table of values for $y=x^2-6x+7$.

Draw the graph of $y=x^2-6x+7$ for $0\le x\le 6$.

Write down the equation of the line of symmetry of the graph.

Use the graph to solve the equation $x^2-6x+7=0$.

Give your answers to 1 decimal place.

Here is the graph of  $y=x^2-5x+3$

Use your graph to find the solutions to  $x^2-6x+5=-3$ 

Complete the table of values for $y=\frac{15}{x}$

On the grid, draw the graph of $y=\frac{15}{x}$ for $-5⩽x⩽-1$ and $1⩽x⩽5$.

Complete the table of values for $y=7+2x-x^2$

On the grid, draw the graph of $y=7+2x-x^2$ for $-2⩽x⩽4.$

Write down the equation of the line of symmetry of the graph.

Complete the table of values for $y=-x^2+x+5$

On the grid, draw the graph of $y=-x^2+x+5$ for $-3⩽x⩽4$.

Write down the coordinates of the highest point of the graph.

Write down the equation of the line of symmetry of the graph.

A sketch of a quadratic curve is shown.

The curve passes through the points $(-2,0)$ and $(4,0)$.

The curve has a minimum point.

Sasha says the minimum value of $y$ is $-9$.

Show that Sasha may not be correct.

Complete the table of values for $y=\frac{8}{x}$.

On the grid, draw the graph of $y=\frac{8}{x}$for $-5⩽x⩽-1$ and $1⩽x⩽5.$

]

i) Complete the table of values for $y=\frac{12}{x},x\ne 0.$

[3]

ii) On the grid, draw the graph of $y=\frac{12}{x}$ for $-6⩽x⩽-1$ and $1⩽x⩽6$.

[4]