A truck can be rented from Company A for $120 a day plus $0.50 per mile. Company B charges $50 a day plus $0.70 per mile to
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Vertex form is
y=a(x-h)^2+k
vertex is (h,k)
axis of symmetry is x=4, therfor h=4
y=a(x-4)^2+k
we have some points
(3,-2) and (6,-26)
input and solve for a and k
(3,-2)
-2=a(3-4)^2+k
-2=a(-1)^2+k
-2=a(1)+k
-2=a+k
(6,-26)
-26=a(6-4)^2+k
-26=a(2)^2+k
-26=a(4)+k
-26=4a+k
we have
-2=a+k
-26=4a+k
multiply first equation by -1 and add to second
2=-a-k
<u>-26=4a+k +</u>
-24=3a+0k
-24=3a
divide both sides by 3
-8=a
-2=a+k
-2=-8+k
add 8 to both sides
6=k
the equation is
y=a(x-h)^2+k
vertex is (h,k)
axis of symmetry is x=4, therfor h=4
y=a(x-4)^2+k
we have some points
(3,-2) and (6,-26)
input and solve for a and k
(3,-2)
-2=a(3-4)^2+k
-2=a(-1)^2+k
-2=a(1)+k
-2=a+k
(6,-26)
-26=a(6-4)^2+k
-26=a(2)^2+k
-26=a(4)+k
-26=4a+k
we have
-2=a+k
-26=4a+k
multiply first equation by -1 and add to second
2=-a-k
<u>-26=4a+k +</u>
-24=3a+0k
-24=3a
divide both sides by 3
-8=a
-2=a+k
-2=-8+k
add 8 to both sides
6=k
the equation is
The value of c for which the considered trinomial becomes perfect square trinomial is: 20 or -20
<h3>What are perfect squares trinomials?</h3>They are those expressions which are found by squaring binomial expressions.
Since the given trinomials are with degree 2, thus, if they are perfect square, the binomial which was used to make them must be linear.
Let the binomial term was ax + b(a linear expression is always writable in this form where a and b are constants and m is a variable), then we will obtain:
Comparing this expression with the expression we're provided with:
we see that:
Thus, the value of c for which the considered trinomial becomes perfect square trinomial is: 20 or -20
Learn more about perfect square trinomials here: