SOLUTION: Identify the min/max (vertex) value. Then sketch the graph. f(x)-x^2-10x-30

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Identify the min/max (vertex) value. Then sketch the graph. f(x)-x^2-10x-30      Log On


   

Question 968610: Identify the min/max (vertex) value. Then sketch the graph.
f(x)-x^2-10x-30
Found 4 solutions by lwsshak3, ikleyn, greenestamps, josgarithmetic:
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Identify the min/max (vertex) value. Then sketch the graph.
f(x)-x^2-10x-30
complete the square:
f(x)-(x^2+10x+25)+25-30
f(x)-(x+5)^2-5
vertex: (-5, -5)
max value=-5
see graph below:
+graph%28+300%2C+300%2C+-20%2C10%2C+-10%2C+10%2C-x%5E2-10x-30%29+

Answer by ikleyn(53876) About Me  (Show Source):
You can put this solution on YOUR website!
.
Identify the min/max (vertex) value. Then sketch the graph.
f(x)-x^2-10x-30
~~~~~~~~~~~~~~~~~~~~~~~~~~~~


The post is written incorrectly and makes no sense.


The algorithm (the computer code) in the post by @lwsshak3 did not recognize the nonsense

and produced incorrect non-sensical gibberish, which @lwsshak3 tries to sell as the solution,

without reading the output of his code.



Answer by greenestamps(13355) About Me  (Show Source):
You can put this solution on YOUR website!


The wording of the post is certainly strange; but the intention is clear: find the vertex.

f%28x%29=-x%5E2-10x-30

Given a quadratic function f%28x%29=ax%5E2%2Bbx%2Bc, the x-coordinate of the vertex is -b%2F%282a%29:

-%28-10%29%2F%282%28-1%29%29=10%2F-2=-5

The y-coordinate of the vertex is found by evaluating the function at that value of x:

f%28-5%29=-%28-5%29%5E2-10%28-5%29-30=-25%2B50-30=-5

ANSWER: The vertex is (-5,-5)

The graph....

graph%28400%2C400%2C-10%2C5%2C-25%2C5%2C-x%5E2-10x-30%29

Answer by josgarithmetic(39823) About Me  (Show Source):
You can put this solution on YOUR website!
Student could have gave minus sign instead of "equals" sign.
f%28x%29=x%5E2-10x-30
and wants vertex, and know if max or min.

Try completing-square.
%2810%2F2%29%5E2=25;
add and subtract from, to the quadratic expression.

x%5E2-10x-30%2B25-25
x%5E2-10x%2B25-30-25
%28x-5%29%5E2-55
highlight%28f%28x%29=%28x-5%29%5E2-55%29
vertex point at (5, -55) and is a minimum.