What are the vertex and x-intercepts of the graph of the function given below?
2 answers:
In order to determine the vertex of this, you can complete the square. To do that, first set the equation equal to 0, then move the -35 over to the other side by adding. That gives us 
. Now we can complete the square. Do this by taking half of the linear term, squaring it, and adding it in to both sides. Our linear term is 2x. Half of 2 is 1, and 1 squared is 1. So we add 1 to both sides, creating something that looks like this: 
. We will do the math on the right and get 36, and the left will be expressed as the perfect square binomial we created by doing this whole process. 
. Now move the 36 over by subtraction and set it back to equal y and your vertex is apparent. It is (1, -36). You find the x-intercepts when y = 0. That means you need to set your original equation equal to zero and factor it. The easiest, surest way to do this is to use the quadratic formula. Doing that gives us x values of 7 and -5. And you're done!
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Step-by-step explanation:
The volume of a cube is
where a is the side length,
Note: If you want to remember this formula, know that a cube is basically a bunch of squares stacked on one another vertically and horizontally
The area of a square with side length a, is
If we multiply that by the height of the cube, which is a.
That is the easy way to derive the formula of the volume of a cube.
Back on track, we know the volume so we must solve for a.
1.
Assuming you took algebra, to isolate the variable a, we must undo it being raised to the third power.
To do this, we take the cube root of both sides
The cube root of 125 is 5 so
5 cm
2.
2 ft
3.
7 yd
4.
10 mm
5.
12 in. or 1 ft
6.
1 m