which statement best describes the effect on the parabola with an equation of y = x² + 4x when it is changed…
which statement best describes the effect on the parabola with an equation of y = x² + 4x when it is changed to y = x² + 6x?\na. the parabola is shifted to the left 2 units.\nb. the parabola is shifted to the right 2 units.\nc. the parabola is shifted up 5 units and to the right 1 unit.\nd. the parabola is shifted down 5 units and to the left 1 unit.
Answer
Explanation:
Step1: Write equations in vertex - form
The vertex - form of a parabola is $y=a(x - h)^2+k$, where $(h,k)$ is the vertex. For $y=x^{2}+4x$, we complete the square: $y=x^{2}+4x=(x + 2)^{2}-4$, so the vertex is $(-2,-4)$. For $y=x^{2}+6x$, we complete the square: $y=x^{2}+6x=(x + 3)^{2}-9$, so the vertex is $(-3,-9)$.
Step2: Analyze the change in the vertex
The $x$ - coordinate of the vertex changes from $-2$ to $-3$ (a change of $-3-(-2)=-1$), which means a shift of 1 unit to the left. The $y$ - coordinate of the vertex changes from $-4$ to $-9$ (a change of $-9-(-4)=-5$), which means a shift of 5 units down.
Answer:
D. The parabola is shifted down 5 units and to the left 1 unit.