The antiderivative does not exist in elementary form.
These type of integrals can be approximated using numerical methods if limits are given.
If you want a more technical response, go to wolframalpha.
Answer:
See below.
Step-by-step explanation:
Equation of parabola:
y = some expression in x^2
To translate the parabola vertically, substitute y with y - k.
The translation is k units vertically. If k is positive, the translation is up. If k is negative the translation is down.
Example 1:
original parabola: y = x^2 - 2x + 5
To translate it 3 units up, we need k = 3.
Substitute y with y - 5 to get
y - 3 = x^2 - 2x + 5
y = x^2 - 2x + 8 is the equation of the parabola translated 3 units up.
Example 2:
original parabola: y = 2x^2 + 4x - 6
To translate it 5 units down, we need k = -5.
Substitute y with y - (-5), or y = 5 to get
y + 5 = 2x^2 + 4x - 6
y = 2x^2 + 4x - 11
y = 2x^2 + 4x - 11 is the equation of the parabola translated 5 units down.
Answer:
jyfkufujfghnghjmgb
Step-by-step explanation:
1. TRUE - anything is symmetric about its axis of symmetry
2. FALSE - they open up or down, depending on the sign of "a"
3. TRUE - the x-coordinate of the vertex is -b/(2a). Its y-coordinate is f(x) at that point.
4. FALSE - for negative "a", the parabola opens downward.
Answer is D. Range is the difference between the largest datum and the smallest datum
