Factorise fully 77x-33x^2
1 answer:
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Refer the attached figure for the graphic representation of the given quadratic equation.
<u>Step-by-step explanation:</u>
Given expression:
To find:
The graphic representation of the given quadratic function
For solution, plot the graph to the given quadratic equation.
The standard form of the equation is
When comparing with given quadratic equation,
a = 1, b = - 8, c = 24
Axis of symmetry is
By applying the values, the axis of symmetry of given equation is
The vertex form of quadratic equation is
Where, (h,k) are the vertex.
Convert the quadratic equation into vertex form.
By completing the square,
On comparison,
(h , k) = (4 , 8)
Now, plot the equation with vertex (4,8) [refer attached figure].
Answer:
<u>Step-by-step explanation:</u>
There are 3 conditions that must be satisfied:
- f(x) is continuous on the given interval
- f(x) is differentiable
- f(a) = f(b)
If ALL of those conditions are satisfied, then there exists a value "c" such that c lies between a and b and f'(c) = 0.
f(x) = x³ - x² - 6x + 2 [0, 3]
1. There are no restrictions on x so the function is continuous
2. f'(x) = 3x² - 2x - 6 so the function is differentiable
3. f(0) = 0³ - 0² - 6(0) + 2 = 2
f(3) = 3³ - 3² - 6(3) + 2 = 2
f(0) = f(3)
f'(x) = 3x² - 2x - 6 = 0
This is not factorable so you need to use the quadratic formula:
Only one of these values (1.8) is between 0 and 3.