1) We can determine by the table of values whether a function is a quadratic one by considering this example:
x | y 1st difference 2nd difference
0 0 3 -0 = 3 7-3 = 4
1 3 10 -3 = 7 11 -7 = 4
2 10 21 -10 =11 15 -11 = 4
3 21 36-21 = 15 19-5 = 4
4 36 55-36= 19
5 55
2) Let's subtract the values of y this way:
3 -0 = 3
10 -3 = 7
21 -10 = 11
36 -21 = 15
55 -36 = 19
Now let's subtract the differences we've just found:
7 -3 = 4
11-7 = 4
15-11 = 4
19-15 = 4
So, if the "second difference" is constant (same result) then it means we have a quadratic function just by analyzing the table.
3) Hence, we can determine if this is a quadratic relation calculating the second difference of the y-values if the second difference yields the same value. The graph must be a parabola and the highest coefficient must be 2
Answer: -4w+32
Step-by-step explanation: 4*-w + 4*8
Answer:
f(x) = 2x^2 - 6x - 20.
Step-by-step explanation:
(-2, 0) and (5, 0) are 2 zeroes of the function so we can write the function as
f(x) = a(x + 2)(x - 5) where a is a constant.
Now as (4, -12) is a point on the graph:
-12 = a(4 + 2)(4 - 5)
-12 = a * 6 * -1
-6a = -12
a = 2.
So f(x) = 2(x + 2)(x - 5)
f(x) = 2x^2 - 6x - 20.
The answer is: Perpendicular, because both equations intersects or cross over each other. There is an attached photo
