Finding a and b for y = ax^2 + bx Passing Through (2,4) with Gradient 8

[tweety1234]

Homework Statement

The curve $$y = ax^{2} + bx$$ passes through the point (2,4) with gradient 8. Find a and b .

I have no idea how to work out a and b , do I use simultaneous equations?

Homework Equations

The Attempt at a Solution

I have no idea how to work out a and b , do I use simultaneous equations?

 

[RoryP]

well start of by thinking about what your dy/dx would be...

 

[tweety1234]

okay so dy/dx = $$2ax + b$$ from this how do I find what a and b equal ?

 

[Mark44]

Use the fact that (2, 4) is a point on the curve in your given equation, which will give you an equation that involves only a and b.

Then use the fact that at x = 2, dy/dx = 8 in your equation for the derivative. This will give you another equation in a and b.

Finally, solve the two equations in a and b simultaneously.

 

[tweety1234]

Use the fact that (2, 4) is a point on the curve in your given equation, which will give you an equation that involves only a and b.

Then use the fact that at x = 2, dy/dx = 8 in your equation for the derivative. This will give you another equation in a and b.

Finally, solve the two equations in a and b simultaneously.

so I just sub in the values for x and y ?

are these two equations correct..

$$4a + b = 4$$

$$4a + b = 8$$

?

 

[danago]

Have another look at the first equation.

 

[tweety1234]

Have another look at the first equation.

x=2 so 2x2=4? can you give more hints, cause I am really stuck

thank you!

 

[tweety1234]

is it meant to be $$32a + b =4$$ ?

 

[Mark44]

is it meant to be $$32a + b =4$$ ?

No.

Write your first equation.
Substitute 2 for x and 4 for y in that equation. The other equation you wrote, 4a + b = 8, is correct.

 

[tweety1234]

$$y = ax^{2} + bx$$ , $$4a + 2b = 4$$ is this correct? so a = 3 and b = -4 ?

 

[HallsofIvy]

Check it yourself. IF a= 3 and b= -4, you have y= 3x²- 4x. What is y when x= 2? What is y' when x= 2?