Graphs 7
2 marks · EasyExplain how you would use a graph to solve the equation x^2 + 2 = 2x.
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.
Show answer
Draw the graphs of y = x^2 + 2 and y = 2x on the same axes. The x-values where the two graphs cross give the solutions to x^2 + 2 = 2x.
Also accept: Draw y = x^2 + 2 and y = 2x and find intersection x-values; Plot y = x^2 + 2 and y = 2x; intersections give solutions
Common mistakes: Only draw y = x^2 + 2
Show mark scheme and worked solution
Marking points
M1 · 1 mark · Mentions drawing both graphs (y = x^2 + 2 and y = 2x) or rearranges equation for intersection.
A1 · 1 mark · States that the x-coordinates of intersection points give the solutions.
Worked solution
To solve x^2 + 2 = 2x graphically, plot y = x^2 + 2 and y = 2x. The points where the two graphs intersect have coordinates (x, y) that make x^2 + 2 = 2x true. The x-values at the intersections are the solutions.