A building has an entry the shape of a parabolic arch 84 ft high and 42 ft wide at the base, as shown below. A parabola opening
2 answers:
Answer:
Step-by-step explanation:
Because of the nature of the information we are given, we have no choice but to use the equation
and solve for a.
We know by the info that the vertex is (0, 84). We also know that if the vertex is at the origin, and that the base is 42 feet wide, it spans 21 feet to the right of the origin and 21 feet to the left of the origin. That means that we have 2 coordinates from which we need to pick one for our x and y in the equation. I don't like negatives, so I am going to choose the coordinate (21, 0) as x and y. Because this parabola opens upside down, as archways of door openings do, our "a" value better come out algebraically as a negative. Let's see...From the vertex we have that h = 0 and k = 84. So filling in:
and simplifying a bit:
0 = 441a + 84 and
-84 = 441a so
Good, a is negative. Your equation is, then:
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Answer:
Step-by-step explanation:
Instead, since the divisor is in the form of , use what is called Synthetic Division. Remember, in this formula,
gives you the OPPOSITE terms of what they really are, so do not forget it. Anyway, here is how it is done:
4| 1 −5 7 −12
↓ 4 −4 12
_______________
1 −1 3 0 →
You start by placing the in the top left corner, then list all the coefficients of your dividend [x³ - 5x² + 7x - 12]. You bring down the original term closest to
then begin your multiplication. Now depending on what symbol your result is tells you whether the next step is to subtract or add, then you continue this process starting with multiplication all the way up until you reach the end. Now, when the last term is 0, that means you have no remainder. Finally, your quotient is one degree less than your dividend, so that 1 in your quotient can be an
, the −1 [
] follows right behind it, and bringing up the rear, comes the 3, giving you the quotient of
.
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