Answer:
Step-by-step explanation:
<u>Given quadratic function:</u>
<u>Points on the graph:</u>
- (-2,-35), (1,-5), (3,- 15)
<u>Substitute values of x and y and solve the system of equations:</u>
- -35 = a(-2)² + b(-2) + c ⇒ -35 = 4a - 2b + c ⇔ eq 1
- -5 = a(1)² + b(1) + c ⇒ -5 = a + b + c ⇔ eq 2
- -15 = a(3)² + b(3) + c ⇒ -15 = 9a + 3b + c ⇔ eq 3
<u>Subtract eq 2 from eq 1:</u>
- -35 - (-5) = 4a - 2b + c - a - b - c
- -30 = 3a - 3b
- b = a + 10 ⇔ eq 4
<u>Subtract eq 2 from eq 3:</u>
- -15 - (-5) = 9a + 3b + c - a - b - c
- -10 = 8a + 2b
- b = -4a - 5 ⇔ eq 5
<u>Compare eq 4 and eq 5, solve for a:</u>
- a + 10 = -4a - 5
- a + 4a = -5 - 10
- 5a = -15
- a = -3
<u>Find the value of b using eq 4:</u>
<u>Find the value of c using eq 2:</u>
- -5 = -3 + 7 + c
- c = -5 - 4
- c = -9
<u>We now have a, b and c:, the function is:</u>
9514 1404 393
Answer:
c. 1150 square units
Step-by-step explanation:
The sum of the two side lengths is half the perimeter, so is 125/2 = 62.5 units. The long side is 4/5 of that, so is 50 units.
The area is the product of the long side and the height to the long side:
A = bh
A = (50 units)(23 units) = 1150 units²
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<em>Additional comment</em>
This geometry is impossible, because the height from the long side cannot be more than the length of the short side. Here, the short side is 12.5 units, so it is not possible for the height to be 23 units.
If the height is measured from the short side, then the area is 287.5 square units.
Step-by-step explanation:
For every increase in the x-value by 1,
the y-value decreases by -2.
(From 3 to 1 and from 1 to -1)
Hence, slope of line k
= Rise/Run = (-2)/1 = -2. (A)
There are two solutions to this question, one is positive and the other is negative:
