Answer:
y ≥ x^2 - 1
Step-by-step explanation:
First, we can see that the shaded region is above what seems to be a parabola, and we also can see that the lines of the parabola are solid lines (which means that the points on the curve itself are solutions, so the symbol ≥ is used)
Then:
y ≥ a*x^2 + b*x + c
where a*x^2 + b*x + c is the general quadratic equation.
Now let's find the equation for the parabola:
f(x) = a*x^2 + b*x + c
We also can see that the vertex of the parabola is at the point (0, -1)
This means that:
f(0) = -1 = a*0^2 + b*0 + c
= -1 = c
then we have that c = -1
Then:
f(x) = a*x^2 + b*x - 1
Now we can look at the graph again, to see that the zeros of the parabola are at +1 and -1
Which means that:
f(1) = 0 = a*1^2 + b*1 - 1 = a + b - 1
f(-1) = 0 = a*(-1)^2 + b*(-1) - 1 = a - b - 1
Then we got two equations:
a + b - 1 = 0
a - b - 1 = 0
from this we can conclude that b must be zero.
Then:
b = 0
and these equations become:
a - 1 = 0
a - 1 = 0
solving for a, we get:
a = 1
Then the quadratic equation is:
f(x) = 1*x^2 + 0*x - 1
f(x) = x^2 - 1
And the inequality is:
y ≥ x^2 - 1
Answer:
Range
Step-by-step explanation:
In statistics, the range of a set of data is the difference between the largest and smallest value in the distribution. It is calculated by subtracting the lowest value from the highest value. The range shows how widely spread out a set of given data is.
Answer:
B and D
Step-by-step explanation:
The quadratic formula is 
. Here a=20, b=-26, and c=8.
Substitute and you'll have:
This means the solutions are 26 - 6/ 40 and 26 + 6/ 40.
It simplifies to 1/2 and 4/5.
