Question

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.

Answer 1

Answer:

a = 2, b = - 5

Step-by-step explanation:

Given

y = ax² + bx

$\frac{dy}{dx}$ is the measure of the slope at x = a

Differentiate each term with respect to x using the power rule

$\frac{d}{dx}$(a$x^{n}$ ) = na$x^{n-1}$

$\frac{dy}{dx}$ = 2ax + b, hence

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

Substitute x = 2 into $\frac{dy}{dx}$

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