What is the vertex of f (x) = 5x^2+20x-16
2 answers:
Answer:
(-2,-16)
Step-by-step explanation:
Given is a function
To find its vertex
We can use completion of squares method
This is in std vertex form of a parabola
From the equation we find that the vertex is
(-2,-16)
Hence vertex is (-2,-16)
Verify:
Derivative of f(x) =f'(x)=10x+20
Equate to 0 to have x=-2
f(-2) = 20-40-16=-36
Thus verified
Answer:
vertex = (- 2, - 36)
Step-by-step explanation:
Given a parabola in standard form : y = ax² + bx + c : a ≠ 0
Then the x- coordinate of the vertex is
= -
f(x) = 5x² + 20x - 16 is in standard form
with a = 5, b = 20 and c = - 16
= -
= - 2
Substitute x = - 2 into f(x) for corresponding y- coordinate
f(- 2) = 5(- 2)² +20(- 2) - 16 = 20 - 40 - 16 = - 36
vertex = (- 2, - 36)
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Answer:
Therefore, equation of the line that passes through (2,2) and is parellel to the line is
Step-by-step explanation:
Given:
a line
To Find:
Equation of line passing through ( 2, 2) and is parellel to the line y=7x
Solution:
...........Given
Comparing with,
Where m =slope
We get
We know that parallel lines have Equal slopes.
Therefore the slope of the required line passing through (2 , 2) will also have the slope = m = 7.
Now the equation of line in slope point form given by
Substituting the points and so we will get the required equation of the line,
Therefore, equation of the line that passes through (2,2) and is parellel to the line is