Help with Quadratics (finding minimum or maximum)

Hello! Trying to help my little brother with his maths. I have completely forgotten everything in higher maths after not doing it for a year I am struggling to help him out... I know this is probably quite simple but I just cannot work it out. This is his national 5 course but this element of the course came up for me in higher, so I thought I could ask for help here.

y=(x-4)^2 -3
a) State the equation of the axis of symmetry
b) Write down the coordinates of the turning point and state whether it is a maximum or minimum.

We have tried finding the equation of the axis of symmetry by using a bunch of stuff, and our answer for x always comes out wrong. The back of the book says the answer for a is x=4 but we can't get that answer.

I would also appreciate some help with b, because in higher maths I had to use a whole bunch of things to find maximums and minimums but it is apparently much simpler for national 5. The book says if a is greater than 0 it is the minimum value, and if it is less than zero it is the maximum... But I have no idea how to even get to that point!

I would appreciate any help, thanks guys.

Reply 1

zed963

16

For part b you would have to differentiate the equation.

Then use what the book says.

1) Expand expression
2) Simplify
3) Differentiate

Reply 2

AKell17

12

For the axis of symmetry, you wanna think about the curve that's created. A quadratic curve follows the equation (x-a)^2 + b = 0, with a stationary point at the co-ordinates (a,b). This particular curve has its lowest point at (4,3). The axis of symmetry for a quadratic cuts through the stationary point (think about the graph) and so it's x=4 :smile:

Reply 3

Super199

20

Original post by zed963

For part b you would have to differentiate the equation.

Then use what the book says.

1) Expand expression
2) Simplify
3) Differentiate

Since we have it in completed form can you not say just the turning point is (4,-3) and that it is a minimum point as we have a positive quadratic?

Reply 4

Ambry

OP

18

My brothers level of maths does not do differentiation, so I think that was the point I was stuck on. Because he does not use differentiation I had no idea how to possibly get a maximum or minimum turning point!
In his book it says 'if a>0, the turning point gives the minimum value of the function, and if a<0, the turning point gives the maximum value of the function.' Is that it? If a is positive it is a minimum value and if it is negative it is a maximum value?

Reply 5

Super199

20

Original post by Ambry

My brothers level of maths does not do differentiation, so I think that was the point I was stuck on. Because he does not use differentiation I had no idea how to possibly get a maximum or minimum turning point!
In his book it says 'if a>0, the turning point gives the minimum value of the function, and if a<0, the turning point gives the maximum value of the function.' Is that it? If a is positive it is a minimum value and if it is negative it is a maximum value?

Yup pretty much. So what do you think the turning point is in this case?

Reply 6

zed963

16

Original post by AKell17

For the axis of symmetry, you wanna think about the curve that's created. A quadratic curve follows the equation (x-a)^2 + b = 0, with a stationary point at the co-ordinates (a,b). This particular curve has its lowest point at (4,3). The axis of symmetry for a quadratic cuts through the stationary point (think about the graph) and so it's x=4 :smile:

(4,-3)

Reply 7

AKell17

12

Original post by zed963

(4,-3)

Oh right yeah :P