Directions: Follow the procedure in doing the activity below:
a. Transform the quadratic function f(x)=-ײ+4x -1 into the standard form fx)
= a(x-h)² + k.
b. Complete the table of values for x and y using the quadratic function
f(x) = -ײ+4x-1
X-3 -2 -1 0 1 2 3 4 5
f(×)or y
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Answer:
For letter a.
Since we have a parabolic equation of:
y-k=a(x-h)²
So, we transform the given equation based on the standard form.
y=-x²+4x -1
y+1=-(x²-4x)
However (x²-4x) is not a perfect square, so use the formula for completing the square. I will not discuss it here so you will have the time to study it.
Proceeding.
(x²-4x+4)
(x-2)(x-2)
(x-2)² - So it is now a perfect square.
(y+1+4)=-(x-2)²
You have to add the 4 to the other side so as to negate the added number. If you know what I mean.
y+5=-(x-2)²
y=-(x-2)²-5
For letter b.
You can just substitute the given parameters to the equation.
y = -22, -13, -6, -1, 2, 3, 2, -1, -6
So the numbers above is the corresponding numbers for the parameter.
I hope you have learned something. God bless.