Question
what is the stretch of y=-2\left(x+4\right)^{2}+3
Answers
Answered by
GPT-4o mini
The equation \( y = -2(x + 4)^2 + 3 \) is in the form of a quadratic function, specifically a parabola.
To identify the stretch and other properties of the parabola, let's break down the components:
1. The term \( (x + 4)^2 \) indicates a horizontal shift of the vertex to the left by 4 units.
2. The coefficient of \( -2 \) in front of the quadratic term indicates that the parabola opens downwards. The absolute value of this coefficient (\( | -2 | = 2 \)) indicates that the parabola is vertically stretched by a factor of 2 compared to the standard parabola \( y = x^2 \).
3. The term \( +3 \) indicates a vertical shift of the vertex up by 3 units.
In summary:
- The parabola opens downward.
- It has a vertical stretch factor of \( 2 \).
- The vertex of the parabola is located at \( (-4, 3) \).
Thus, the stretch of the parabola represented by the equation \( y = -2(x + 4)^2 + 3 \) is a vertical stretch by a factor of \( 2 \).
To identify the stretch and other properties of the parabola, let's break down the components:
1. The term \( (x + 4)^2 \) indicates a horizontal shift of the vertex to the left by 4 units.
2. The coefficient of \( -2 \) in front of the quadratic term indicates that the parabola opens downwards. The absolute value of this coefficient (\( | -2 | = 2 \)) indicates that the parabola is vertically stretched by a factor of 2 compared to the standard parabola \( y = x^2 \).
3. The term \( +3 \) indicates a vertical shift of the vertex up by 3 units.
In summary:
- The parabola opens downward.
- It has a vertical stretch factor of \( 2 \).
- The vertex of the parabola is located at \( (-4, 3) \).
Thus, the stretch of the parabola represented by the equation \( y = -2(x + 4)^2 + 3 \) is a vertical stretch by a factor of \( 2 \).