1 of 8 0-day streak

Intersections of a line and a quadratic graph

Question 1 of 8

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Consider the line and quadratic graph with rules

y=-x + 5

y=-3x^2 + 23x - 31

Use exact values. A common point has the same x- and y-values in both rules

(a)1 mark

Which equation in x correctly represents the common points of the two graphs?

-x + 5=0

-3x^2 + 23x - 31=0

-3x^2 + 24x - 36=0

(b)1 mark

Calculate the discriminant of the combined quadratic equation

\(\Delta\)

Before finding the coordinates, use the discriminant of the combined equation to choose the number of common points

2 common points

1 common point

0 common points

(d)4 marks

Report the common points of the line and quadratic graph as ordered pairs

Enter the point with the smaller x-coordinate first

\(x_1\) \(y_1\) \(x_2\) \(y_2\)