Answer:
f(x) = 2x(x - 8)
f(x) = 2(x - 2)² - 8
Step-by-step explanation:
Let the equation of the quadratic function is,
f(x) = a(x - h)² + k
Here, (h, k) is the vertex of the function.
From the graph attached,
Vertex of the parabola → (2, -8)
Therefore, equation of the function will be,
f(x) = a(x - 2)² - 8
Since, the graph passes through origin (0, 0),
f(0) = a(0 - 2)² - 8
0 = 4a - 8
a = 2
Equation of the given parabola will be,
f(x) = 2(x - 2)² - 8
= 2(x² - 4x + 4) - 8
= 2x² - 8x + 8 - 8
= 2x² - 8x
= 2x(x - 8)
Therefore, factored form of the function will be,
f(x) = 2x(x - 8)
Answer:
178
Step-by-step explanation:
area of big rectangle : 143
area of small rectangle:20
area of triangle : 15
143+20+15= 178
Given data:
X Y
1 0
2 - 2
3 - 4
4 - 6
From the above table,
We have to see what sort of function is it showing.
Therefore,
Taking the first difference of the y-values.
We get,
-2 , -2 , -2
The first difference is constant for all the y-values, that is -2. Therefore it is a linear function,
So,
using the general form,
y = mx + b
where m represent the slope and b represents the y-intercept.
Now,
We will use two coordinate points to find out the slope,
Let them be: (1,0) and (2,-2)
So,
m = 2 / -1
m = -2
Now the y-intercept,
As we know that,
y = -2x + b
Take any point from the table, let it be (1,0)
substituting it into the equation, we get;
0 = -2(1) + b
b = 2
Hence our equation is:
y = - 2x + 2
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