which statement describes the effect on the parabola $f(x)=2x^{2}-5x + 3$ when it is changed to…

which statement describes the effect on the parabola $f(x)=2x^{2}-5x + 3$ when it is changed to $f(x)=2x^{2}-5x + 1$?\na. the parabola is translated up 1 unit.\nb. the parabola is translated up 2 units.\nc. the parabola is translated down 1 unit.\nd. the parabola is translated down 2 units.

which statement describes the effect on the parabola $f(x)=2x^{2}-5x + 3$ when it is changed to $f(x)=2x^{2}-5x + 1$?\na. the parabola is translated up 1 unit.\nb. the parabola is translated up 2 units.\nc. the parabola is translated down 1 unit.\nd. the parabola is translated down 2 units.

Answer

Explanation:

Step1: Analyze the constant - term change

The original function is $f(x)=2x^{2}-5x + 3$ and the new function is $f(x)=2x^{2}-5x + 1$. The constant - term in the original function is $3$ and in the new function is $1$.

Step2: Calculate the change in the constant - term

The change in the constant - term is $\Delta c=1 - 3=-2$.

Step3: Determine the vertical translation

For a quadratic function $y = ax^{2}+bx + c$, a change in the value of $c$ results in a vertical translation. If $\Delta c>0$, the parabola is translated up; if $\Delta c<0$, the parabola is translated down. Since $\Delta c=-2<0$, the parabola is translated down 2 units.

Answer:

D. The parabola is translated down 2 units.