I have a test tomorrow and I really don't get this, please help me.
"Use transformations and the zeros of the quadratic function f(x)=(x-6)(x+4) to determine the zeros of each of the following functions
a) y=2f(x) b) y=f(2x) c) y=f(0.5x)"
I am so lost, I don't get what it means by 'the zeros', please, please, please help me!
I really don't understand this, I don't mean to be a pain, but I really need to understand this.
Of course, I'll be happy to help you understand the concept and solve these problems!
In mathematics, the zeros of a function refer to the values of x for which the function equals zero, or in other words, the x-values where the function intersects or touches the x-axis. These points are also known as the roots or solutions of the function.
Now let's go through each part of the question and see how we can use transformations and the zeros of the given quadratic function f(x) = (x - 6)(x + 4) to determine the zeros of the new functions.
a) y = 2f(x):
To find the zeros of this function, we need to multiply each zero of f(x) by the factor of 2. This is because multiplying a function by a constant affects the y-values but does not change the x-values or the zeros.
So, the zeros of y = 2f(x) would be:
Zero 1: 2(6) = 12 (since the zero of f(x) is 6)
Zero 2: 2(-4) = -8 (since the zero of f(x) is -4)
Therefore, the zeros of y = 2f(x) are x = 12 and x = -8.
b) y = f(2x):
To determine the zeros of this function, we need to divide each zero of f(x) by the factor of 2. This is because dividing the input values (x) by 2 affects the x-values but doesn't change the y-values or the zeros.
So, the zeros of y = f(2x) would be:
Zero 1: 6/2 = 3 (since the zero of f(x) is 6)
Zero 2: (-4)/2 = -2 (since the zero of f(x) is -4)
Therefore, the zeros of y = f(2x) are x = 3 and x = -2.
c) y = f(0.5x):
To find the zeros of this function, we need to multiply each zero of f(x) by the factor of 0.5 or (1/2). Multiplying the input values (x) by 0.5 affects the x-values but doesn't change the y-values or the zeros.
So, the zeros of y = f(0.5x) would be:
Zero 1: 6 * 0.5 = 3 (since the zero of f(x) is 6)
Zero 2: (-4) * 0.5 = -2 (since the zero of f(x) is -4)
Therefore, the zeros of y = f(0.5x) are x = 3 and x = -2.
I hope this explanation helps you understand how to determine the zeros of each function using transformations and the zeros of the quadratic function. Good luck with your test!