Remember that the vertex form of a parabola or quadratic equation is:
y=a(x-h)^2+k, where (h,k) is the "vertex" which is the maximum or minimum point of the parabola (and a is half the acceleration of the of the function, but that is maybe too much :P)
In this case we are given that the vertex is (1,1) so we have:
y=a(x-1)^2+1, and then we are told that there is a point (0,-3) so we can say:
-3=a(0-1)^2+1
-3=a+1
-4=a so our complete equation in vertex form is:
y=-4(x-1)^2+1
Now you wish to know where the x-intercepts are. x-intercepts are when the graph touches the x-axis, ie, when y=0 so
0=-4(x-1)^2+1 add 4(x-1)^2 to both sides
4(x-1)^2=1 divide both sides by 4
(x-1)^2=1/4 take the square root of both sides
x-1=±√(1/4) which is equal to
x-1=±1/2 add 1 to both sides
x=1±1/2
So x=0.5 and 1.5, thus the x-intercept points are:
(0.5, 0) and (1.5, 0) or if you like fractions:
(1/2, 0) and (3/2, 0) :P
Answer:
A fruit stand has to decide what to charge for their produce.
They need $ 5.30 for 1 apple and 1 orange.
They also need $ 7.30 for 1 apple and 2 oranges.
TO DETERMINE
To put this information into a system of linear equations.
TO find a unique price for an apple and an orange
EVALUATION
Let the price of an apple = x and price of an orange = y
So From the first condition that they need $ 5.30 for 1 apple and 1 orange we get
\sf{x + y = 5.30}x+y=5.30 - - - - Equation 1
Again from second condition that they need $ 7.30 for 1 apple and 2 oranges we get
\sf{x + 2y = 7.30}x+2y=7.30 - - - - Equation 2
So the required Set of linear equations are
x + y = 5.30
x + 2y = 7.30
Equation (2) - Equation (1) we get
y = 2
From Equation (1) we get
x = 5.30 - 2 = 3.30
Hence price of an apple = $ 3.30
The price of an orange = $ 2
The inequality would be 50w + 100 >_ 18,000 ( the _ goes under the > but I cannot do that on my phone )
Answer:
Step-by-step explanation:
-3 from all ends to get 1<-3x<3 then divide by -3 on all ends to get -1/3>x>-1 you flip the sign because of the negative,
