Graphs 7

4 marks · Normal

The graph below shows the curve for .

Graph of \( y = x^2 - 4x + 2 \) on \( 0 \leq x \leq 5 \)

(a)

Use the graph to estimate the solutions of for .

[2 marks]

(b)

By drawing a suitable straight line on the graph, use it to solve the equation for .

[2 marks]

Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.

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(a) —

(b) —

Also accept: Accept estimates within 0.1 of correct values by reading the graph.

Common mistakes: Confusing x and y values, or giving points rather than x coordinates only.

Show mark scheme and worked solution

Marking points

M1 (a) · 1 mark · Estimates the x-values where curve crosses y=0.

A1 (a) · 1 mark · Both answers to 1 decimal place, within reading tolerance.

M2 (b) · 1 mark · Draws or visualises the horizontal line y = 3 and finds intersections.

A2 (b) · 1 mark · States both x-values where y=3 within graph, correct to 1 decimal place.

Worked solution

a) From the graph, when , the curve crosses at approximately and .

b) Draw the line . This meets the curve at approximately and (to 1 decimal place).