Given that x 2 2x 3 (x a) 2 b, a find the value of the constants a and b b Sketch the graph of y x 2 2x 3, indicating clearly the coordinates of any intersections with the coordinate axes c Find the value of the discriminant of x 2 2x 3 Explain how the sign of the discriminant relates to your sketch in part b The equation x 2 k x 3 0, where k is a constant, has no real roots d Find the set of possible values of k, giving your answer in surd form

Question: Given that x 2 + 2x + 3 (x + a) 2 + b, a. find the value of the constants a and b. b.

Given that x² + 2x + 3 (x + a)² + b,

a. find the value of the constants a and b.

b. Sketch the graph of y = x² + 2x + 3, indicating clearly the coordinates of any intersections with the coordinate axes.

c. Find the value of the discriminant of x² + 2x + 3. Explain how the sign of the discriminant relates to your sketch in part b. The equation x² + k_x + 3 = 0, where k is a constant, has no real roots.

d. Find the set of possible values of k, giving your answer in surd form.

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a To find the values of the constants a and b we can expand the expression x a b x a b x 2ax a b Com... View full answer

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