# Determine without graphing

posted by .

Determine without graphing, whether the given function has a maximum value and then find the value. f(x)=3x^2+30x-1

• Determine without graphing -

http://www.jiskha.com/display.cgi?id=1363360907

What part of his answer did you not like ?

• Determine without graphing -

I needed help learning how to find the value.

• Determine without graphing -

f(x) = 3(x^2 + 10x +25)-76
= 3(x+5)^2 -76

The function has no maximum. It has a minimum of -76 when x = -5.

• Determine without graphing -

Hmmm. I explained that there is no maximum value. Don't expect to be able to find it.

Now, if you want to find the minimum value, try completing the square:

3x^2+30x-1
= 3(x^2 + 10x) - 1
= 3(x^2 + 10x + 25) - 1 - 75
That step is the key. We added 75 to complete the square, so we have to subtract it as well to avoid changing f(x)
= 3(x+5)^2 - 76

Now you can see that since (x+5)^2 is always at least zero (since squares are never negative), the smallest value for (x+5)^2 is when x = -5. In that case, f(x) = 3(0) - 76

So, f(-5) = -76, and it can never be less than that, because whatever x is, (x+5)^2 will be some positive number, making f(x) > -76

## Similar Questions

1. ### Algebra

This will be a multiple post thing so please bear with me. If my answers are wrong then please explain I'll post my work as needed thanks. 1)Identify the y-intercept and the axis of symemetry for the graph of f(x)=-3x^2+6x+12. answer=12:x=1 …
2. ### algebra

1)Identify the y-intercept and the axis of symemetry for the graph of f(x)=-3x^2+6x+12. answer=12:x=1 2)Determine whether f(x)=-5x^2-10x+6 has a maximum or minimum value and find that value. answer=maximum -1 3)Solve x^2=4x by graphing …
3. ### Algebra- Maximum and minimum.

I don't understand how to find the maximum and minimum. Determine whether the given quadratic function has a minimum value or maximum value. Then find the coordinates of the minimum or maximum point. 15.f(x) = -x2 + 2x - 4 20.f(x) …
4. ### urgent math

without graphing, find the vertex, the azis of symemtry, and the maximum value or the minium value.
5. ### College algebra

Determine without graphing, whether the given function has a maximum value and then find the value. f(x)=3x^2+18x-6
6. ### math

Determine whether the given quadratic function has a minimum value or maximum value. Then find the coordinates of the minimum or maximum point.f(x) = x2 + 2x - 9
7. ### Algebra 2

Without graphing, identify the verx, axis of symmetry, and transformations from the parent function f(x)= absolute value of x y= 4- absolute value of x-2
8. ### Algebra Help

Determine without graphing, whether the given quadratic function has a max value or min value and then find the value. F(x)=2x^2+16x-1
9. ### calculus

Use a graphing utility to graph the function and find the absolute extrema of the function on the given interval. (Round your answers to three decimal places. If an answer does not exist, enter DNE.) f(x) = x^4 − 2x^3 + x + 1, …
10. ### Calculus

Find the minimum value of the following function: h(x)= x-(12(x+1)^(1/3) -12) on the interval [0, 26] Honestly, I have found by graphing that the minimum value is at the coordinate point (9,-3), but I need to do this in a way that …

More Similar Questions