The curve with equation y=ax^2+bx has a gradient of 3 at the point (2,-2). find the values of a and b.

a = 2, b = - 5

Step-by-step explanation:

Given

y = ax² + bx

is the measure of the slope at x = a

Differentiate each term with respect to x using the power rule

(a ) = na

= 2ax + b, hence

2ax + b = 3 at (2, - 2)

Substitute x = 2 into

4a + b = 3 → (1) and substitute x = 2 into y

4a + 2b = - 2 → (2)

Subtract ( 1) from (2)

b = - 2 - 3 = - 5

Substitute b = - 5 into (1)

4a - 5 = 3 ( add 5 to both sides )

4a = 8 ( divide both sides by 4 )

a = 2

{3 + i, 3 - i, 3, -1}

step-by-step explanation:

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