Graphs 7
3 marks · EasyThe equations y = x^2 - 3 and y = 2x + 1 are drawn on the same set of axes.
Write down the equation formed by setting the two expressions for y equal to each other.
How many solutions are there to the simultaneous equations y = x^2 - 3 and y = 2x + 1?
Explain what the points of intersection of these two graphs represent.
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(a) x^2 - 3 = 2x + 1
(b) 2
(c) The points of intersection represent the solutions to the simultaneous equations, i.e., the values of x and y that satisfy both equations.
Show mark scheme and worked solution
Marking points
B1 (a) · 1 mark · Forms the correct equation x^2 - 3 = 2x + 1.
B1 (b) · 1 mark · States there are 2 solutions.
B1 (c) · 1 mark · Explains the intersection points are where both equations are satisfied.
Worked solution
a) Setting the two equations equal: x^2 - 3 = 2x + 1 b) This is a quadratic equation which generally gives 2 real solutions: 2 c) The points of intersection are the solutions (x, y) that satisfy both equations at the same time.