Sec 2 Maths · Quadratic equations and graphs

Reading a quadratic graph questions with answers

Practice questions on reading a quadratic graph, from the basics up to exam level, each with a full worked solution. Try them on paper first, then open the solution to check your working.

Worked example

The diagram shows the graph of $y = x^{2} - 6x + 7$ . Use the graph to find the value of $y$ when $x = 4$ .

Step 1 of 1

Start at the given x on the x-axis. Go up or down to the curve, then across to the y-axis

From

x = 4

, go down to the curve, then across to the

y

-axis.

y = -1

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Questions

Question 1The y-value at a given x
The diagram shows the graph of $y = -x^{2} + x + 7$ . Use the graph to find the value of $y$ when $x = 0$ .
Show the worked solution
1. Step 1: Start at the given x on the x-axis. Go up or down to the curve, then across to the y-axisFrom $x = 0$ , go up to the curve, then across to the $y$ -axis. $y = 7$
Question 2The x-values for a given y
The diagram shows the graph of $y = x^{2} - x - 4$ . Use the graph to find the values of $x$ when $y = -2$ .
Show the worked solution
1. Step 1: Draw the horizontal line y = -2 across the graphThe line $y = -2$ meets the curve at two points.
2. Step 2: From each point, go down (or up) to the x-axis and read the x-coordinate $x = -1$ or $x = 2$
Question 3Where the curve crosses the x-axis
The diagram shows the graph of $y = -x^{2} - 5x - 4$ . Write down the $x$ -coordinates of the points where the curve crosses the $x$ -axis.
Show the worked solution
1. Step 1: Read the x-coordinate of each point where the curve crosses the x-axis (there, y = 0)The curve crosses the $x$ -axis at $x = -4$ and $x = -1$ .
Question 4The minimum or maximum point
The diagram shows the graph of $y = -x^{2} - 2x + 5$ . Write down the coordinates of the maximum point of the curve.
Show the worked solution
1. Step 1: The maximum point is the highest point of the curve: read across first, then up or downThe maximum point is $(-1, 6)$ .
Question 5The line of symmetry
The diagram shows the graph of $y = -x^{2} + 6x - 5$ . Write down the equation of the line of symmetry of the curve.
Show the worked solution
1. Step 1: The line of symmetry is the vertical line through the maximum pointThe maximum point is at $x = 3$ .The line of symmetry is $x = 3$ .

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Worked example

The diagram shows the graph of

y = x^{2} - 6x + 7

. Use the graph to find the value of

y

when

x = 4

Step 1 of 1

Start at the given x on the x-axis. Go up or down to the curve, then across to the y-axis

From

x = 4

, go down to the curve, then across to the

y

-axis.

y = -1

Questions

Question 1The y-value at a given x

The diagram shows the graph of $y = -x^{2} + x + 7$ . Use the graph to find the value of $y$ when $x = 0$ .

Show the worked solution

Step 1: Start at the given x on the x-axis. Go up or down to the curve, then across to the y-axisFrom $x = 0$ , go up to the curve, then across to the $y$ -axis. $y = 7$

Question 2The x-values for a given y

The diagram shows the graph of $y = x^{2} - x - 4$ . Use the graph to find the values of $x$ when $y = -2$ .

Show the worked solution

Step 1: Draw the horizontal line y = -2 across the graphThe line $y = -2$ meets the curve at two points.
Step 2: From each point, go down (or up) to the x-axis and read the x-coordinate $x = -1$ or $x = 2$

Question 3Where the curve crosses the x-axis

The diagram shows the graph of $y = -x^{2} - 5x - 4$ . Write down the $x$ -coordinates of the points where the curve crosses the $x$ -axis.

Show the worked solution

Step 1: Read the x-coordinate of each point where the curve crosses the x-axis (there, y = 0)The curve crosses the $x$ -axis at $x = -4$ and $x = -1$ .

Question 4The minimum or maximum point

The diagram shows the graph of $y = -x^{2} - 2x + 5$ . Write down the coordinates of the maximum point of the curve.

Show the worked solution

Step 1: The maximum point is the highest point of the curve: read across first, then up or downThe maximum point is $(-1, 6)$ .

Question 5The line of symmetry

The diagram shows the graph of $y = -x^{2} + 6x - 5$ . Write down the equation of the line of symmetry of the curve.

Show the worked solution

Step 1: The line of symmetry is the vertical line through the maximum pointThe maximum point is at $x = 3$ .The line of symmetry is $x = 3$ .