Question #010fe
1 Answer
Transform the equation to factored form, and answer the following questions.
Explanation:
Basically, what they're asking is to transform the equation to vertex form, and answer the following questions using the now-transformed equation.
#f(x)=1/2x^2+1/2x-10#
Intercept Form
Intercept form is another way to say factored form. This involves factoring.
First, let's factor out the GCF -
#f(x)=1/2x^2+1/2x-10#
#f(x)=1/2(x^2+x-20)#
Now it's a simple trinomial. "What two numbers added equal
In this case, it is
#f(x)=1/2(x+5)(x-4)#
This is the factored form (AKA intercept form).
If we expand the brackets, we will get the standard form.
Zeros
In order to find the
#x = (-b+-sqrt(b^2-4ac))/(2a)#
Here, we sub in the values from a standard equation.
#x = (-(1/2)+-sqrt((1/2)^2-4(1/2)(-10)))/(2(1/2))#
We simplify.
#x = (-1/2+-sqrt(81/4))/(1)#
And solve for
#x [+] = 4#
#x [-] = -5#
If we graph it, we can conclude that the zeros are
Vertex
To find the vertex, in my opinion, the easiest way is to complete the square.
First, we factor out the
#f(x)=1/2x^2+1/2x-10#
#f(x)=1/2(x^2+x)-10#
Now, we divide the
#f(x)=1/2(x^2+x + 1/4 - 1/4)-10#
Now we expand the
#f(x)=1/2(x^2+x + 1/4) -1/8 -10#
Now we simplify the equation.
#f(x)=1/2(x + 1/2)^2 -81/8#
That's our vertex form. If we expand it, we would get the standard form.
Since we have our vertex formula, we can just use the
Thus, the vertex is
If we graph it, we can conclude the that vertex is indeed
Axis of Symmetry
The axis of symmetry is basically the
Thus, it is:
Here's a graph.
graph{1/2x^2+1/2x-10 [-10, 10, -5, 5]}
Hope this helps :)