Question
Write the equation of quadratic function in vertex form with the following transformation: Vertical shrink of 2, right 6 units, and down 3 units. (1 point) Responses y=2(x−6)2−3 y is equal to 2 times open paren x minus 6 close paren squared minus 3 y=12(x−6)2−3 y is equal to 1 half times open paren x minus 6 close paren squared minus 3 y=12(x+6)2+3 y is equal to 1 half times open paren x plus 6 close paren squared plus 3 y=12(x+6)2−3
Answers
Answered by
GPT-4o mini
To write the equation of a quadratic function in vertex form, you'll want to use the form:
\[ y = a(x-h)^2 + k \]
where \((h, k)\) is the vertex of the parabola and \(a\) controls the width and direction of the parabola.
Given the transformations:
1. **Vertical shrink of 2**: This means \( a = \frac{1}{2} \) since a vertical shrink by a factor of 2 means we have a fraction of 1/2 in front.
2. **Right 6 units**: This means \( h = 6 \), so we will replace \(x\) with \((x - 6)\).
3. **Down 3 units**: This means \( k = -3 \).
Putting it all together, the vertex form of the quadratic function is:
\[ y = \frac{1}{2}(x - 6)^2 - 3 \]
Thus, the correct answer is:
\[ y = \frac{1}{2}(x - 6)^2 - 3 \]
This matches with the third option you provided:
\[ y = \frac{1}{2}(x - 6)^2 - 3 \]
\[ y = a(x-h)^2 + k \]
where \((h, k)\) is the vertex of the parabola and \(a\) controls the width and direction of the parabola.
Given the transformations:
1. **Vertical shrink of 2**: This means \( a = \frac{1}{2} \) since a vertical shrink by a factor of 2 means we have a fraction of 1/2 in front.
2. **Right 6 units**: This means \( h = 6 \), so we will replace \(x\) with \((x - 6)\).
3. **Down 3 units**: This means \( k = -3 \).
Putting it all together, the vertex form of the quadratic function is:
\[ y = \frac{1}{2}(x - 6)^2 - 3 \]
Thus, the correct answer is:
\[ y = \frac{1}{2}(x - 6)^2 - 3 \]
This matches with the third option you provided:
\[ y = \frac{1}{2}(x - 6)^2 - 3 \]