1.
the x value of the vertex in form
ax^2+bx+c=y
is
-b/2a
so
-2x^2+8x-18
x value of vertex is
-8/(2*-2)=-8/-4=2
plug it in to get y value
-2(2)^2+8(2)-18
-2(4)+16-18
-8-2
-10
vertex is at (2,-10)
or you could complete the square to get into y=a(x-h)^2+k, where the vertex is (h,k)
so as follows
y=(-2x^2+8x)-18
y=-2(x^2-4x)-18
y=-2(x^2-4x+4-4)-18
y=-2((x-2)^2-4)-18
y=-2(x-2)^2+8-18
y=-2(x-2)^2-10
vertex is (2,-10)
5.
vertex is the time where the speed is the highest
at about t=10, the speed is at its max
Answer:
The value of x is 3.
Step-by-step explanation:
Matthew earned 7500 of 15000, which is exactly half the total amount, meaning that the fraction corresponding to his earnings is 1/2.
Rate of 5:2:x, with number 5 corresponding to Matthew, mean that his fraction of the earnings, in function of x is given by:

Both fractions are equal, so:

Applying cross multiplication:



The value of x is 3.