Question

Determine whether the graph of y = x2 − 6x + 3 has a maximum or minimum point, then find the maximum or minimum value.

Answer 1

I don't have access to graphing calculator either!

Answer 2

This is a parabola opening up because the coefficient on the x^2 term (an implied +1) is positive. So it will have a minimum but no maximum. It can be found with either simple algebra (completing the square) or differential calculus. Both ways are relatively easy. Which way do you prefer?

Answer 3

Simple algebra will be fine

Answer 4

Do you know how to complete the square? I can outline a general procedure on how to do this if you are not familiar with the method.

Answer 5

no please show me

Answer 6

Start with the format of the equation you have: y = ax^2 + bx + c This equals y = a[x^2 + (b/a)x] + c Take half of b/a and square it, adding and subtracting it to the right side so you still have the same equation. y = a[x^2 + (b/a)x + (b^2)/(4a)] + c - (b^2)/(4a) Get the square expression of the expression in brackets: y = a[x + (b/a)]^2 + c - (b^2)/(4a) Now, this is essentially the same (just rewritten) as your original equation. Works the same way. Graphs the same way. Same domain and range. It's the same. But now, we can see that the smallest value for [x + (b/a)]^2 is 0 and that is when x = -b/a, so the smallest the whole right side can be is c - (b^2)/(4a) and that is for y and that is when x = -b/a.

Answer 7

sorry, slight typo. Read this post instead: Start with the format of the equation you have: y = ax^2 + bx + c This equals y = a[x^2 + (b/a)x] + c Take half of b/a and square it, adding and subtracting it to the right side so you still have the same equation. y = a[x^2 + (b/a)x + (b^2)/(4a)] + c - (b^2)/(4a) Get the square expression of the expression in brackets: y = a[x + (b/2a)]^2 + c - (b^2)/(4a) Now, this is essentially the same (just rewritten) as your original equation. Works the same way. Graphs the same way. Same domain and range. It's the same. But now, we can see that the smallest value for [x + (b/2a)]^2 is 0 and that is when x = -b/2a, so the smallest the whole right side can be is c - (b^2)/(4a) and that is for y and that is when x = -b/2a.