A line contains the points (8, 9) and (–12, –7). Using point-slope form, write the equation of the line that is parallel to the
1 answer:
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Answer:
(4,1)
Step-by-step explanation:
The vertex of the quadratic can be found using -b/2a. The vertex is the point (-b/2a, f(-b/2a)).
To find the x coordinate of the quadratic, define its a,b, and c. The quadratic has a = 2, b=-16, and c=31. Then -b/2a is -(-16)/2(2) = 16/4 = 4.
To find the y-coordinate, input the x=4 and solve for y.
The vertex is (4,1).
Answer:
The vertex of the function is the point
The graph increase over the interval--------> (-3,∞)
Step-by-step explanation:
we have
<u>1) Convert to vertex form</u>
Group terms that contain the same variable, and move the constant to the opposite side of the equation
Complete the square. Remember to balance the equation by adding the same constants to each side
Rewrite as perfect squares
-----> function in vertex form
<u>2) Find the vertex</u>
The vertex of the function is the point
<u>3) Find the axis of symmetry</u>
we know that
In a vertical parabola, the axis of symmetry is equal to the x-coordinate of the vertex
The x-coordinate of the vertex in this problem is equal to
therefore
the equation of the axis of symmetry is
<u>4) Find the increase-decrease intervals</u>
The graph increase over the interval--------> (-3,∞)
The graph decrease over the interval--------> (-∞,-3)
see the attached figure to better understand the problem
<u>5) Find the x-intercepts of the function</u>
we know that
the x-intercepts are the values of x when the value of the function is equal to zero
In this problem the x-intercepts are
and
so
The function cross the x-axis twice
see the attached figure
