Determine if each of the statements about the given equation f(x) is true or false.

Question

the equation f(x)=-1/2(x+5)^2+3

the statements

Translated 3 units down

Flipped over the x-axis

Compressed by a factor 1/2

Translated 5 units right

Answer 1

Hi Valentina,

Based on the equation: f(x)=-1/2(x+5)^2+3 I will walk you through how to determine whether the given statements are true or false.

This type of equation is that of a parabola in vertex form. The original equation for a parabola is f(x)= a (x-h)^2 + k . In this equation "a" describes the stretch value of the parabola while the negative or positive value determines if it will open up or down. The "h" resembles the horizontal translation value of the vertex of this parabola from (0,0). Lastly the "k" represents the vertical translation value for the vertex of this parabola. Now that we know the parts of our equation lets get into the questions:

1. Translated 3 units down - No, the parabola is not translated 3 units down. Because the equation says "+3" it will instead be translated up 3 units.
2. Flipped over the x-axis- Yes, in this equation there is a negative "a" value which means the equation will be flipped over the x-axis
3. Compressed by a factor 1/2- Yes, this equation is compressed by a factor of 1/2 because that is the "a" value
4. 5 units right- No, this equation will be translated 5 units to the left. Because the equation says "(x+5)" and the original equation is "(x-h)" it will be translated to the left because in order for the resulting equation to be "(x+5)", the inputted h value must have been negative.