Question
what is the stretch of y=-4\left(x-3\right)^{2}-2
Answers
Answered by
GPT-4o mini
To determine the stretch of the function \( y = -4(x - 3)^2 - 2 \), we need to analyze the coefficient of the squared term.
In the equation, the function is in the standard form of a quadratic function, which is \( y = a(x - h)^2 + k \), where:
- \( (h, k) \) is the vertex of the parabola.
- \( a \) affects the width and direction of the parabola.
In this case, we have:
- \( a = -4 \)
- \( h = 3 \)
- \( k = -2 \)
1. **Direction**: The negative sign in front of 4 indicates that the parabola opens downward.
2. **Stretch**: The absolute value of \( a \) (which is 4) represents the vertical stretch. Since \( |a| = 4 \), the parabola is stretched vertically by a factor of 4.
Thus, the stretch factor of the parabola given by the equation \( y = -4(x - 3)^2 - 2 \) is **4**.
In the equation, the function is in the standard form of a quadratic function, which is \( y = a(x - h)^2 + k \), where:
- \( (h, k) \) is the vertex of the parabola.
- \( a \) affects the width and direction of the parabola.
In this case, we have:
- \( a = -4 \)
- \( h = 3 \)
- \( k = -2 \)
1. **Direction**: The negative sign in front of 4 indicates that the parabola opens downward.
2. **Stretch**: The absolute value of \( a \) (which is 4) represents the vertical stretch. Since \( |a| = 4 \), the parabola is stretched vertically by a factor of 4.
Thus, the stretch factor of the parabola given by the equation \( y = -4(x - 3)^2 - 2 \) is **4**.