Answer
y = 1(x +1) - 3
Explanation
A quadratic equation of the form y = ax^2 + bx + c
This written in complete the square form provides you with the vertex (either a maximum or minimum point depending on the equation).
This results in y = a(x + p) + q
Where - p is the x value and q is the y value of turning point.
For graph 22, x = -1 and y = -3
Therefore, the equation is of the form
y = a(x + 1) - 3 (*)
We still need the value a, this can be obtained by using the y-intercept we are given.
We are told x = 0 when y = -2
Substitute this in (*) equation:
-2 = a(0+1) - 3
-2 = a - 3
a = 1
Therefore final equation is
y = 1(x +1) - 3
This should provide you with the train of thought of how the second question should also be tackled.
If unsure about why the equation
y = a(x + p) + q gives the vertex ask in comments I will respond
Answer:
-3/2
Step-by-step explanation:
Given two points, we can find the slope by
m = (y2-y1)/(x2-x1)
= (-7 - -1)/ (5-1)
= (-7+1)/(5-1)
= -6/4
= -3/2
Point slope form equation: y - y1 = m(x - x1)
in this case
y - 3 = 1.5(x - 4)
Answer
Point slope form equation:
y - 3 = 1.5(x - 4)
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1 foot is 12 inches
Thus 2 feet is 24 inches
Substitute values into equation:
volume = 24 x 24 x 24
volume = 13824
Your answer is option D
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