Question

The graph of which of the following equations is symmetrical about the y-axis?

1. $y=x^2+3x-1$
2. $y=-x^2+x$
3. $y=6x^2+9$
4. $y=3x^2-3x+1$

Short answer

C. Among the given equations, the graph which is symmetrical about the y-axis is $y=6x^2+9$.

Step-by-step solution

Step 1. Given Information.

Given to determine which among the given equations is symmetrical about the y-axis.

Step 2. Explanation.

The equation of y-axis is x=0

For an equation of the form $f\left(x\right)=a{x}^2+bx+c$, the axis of symmetry is given by $x=-\frac{b}{2a}$

For $y=x^2+3x-1$:

The axis of symmetry is:

$\begin{array}{l}x=-\frac{b}{2a}\\ x=-\frac{3}{2\left(1\right)}\\ x=-\frac{3}{2}\end{array}$

Hence the graph is not symmetrical about y axis.

For $y=-x^2+x$:

The axis of symmetry is:

$\begin{array}{l}x=-\frac{b}{2a}\\ x=-\frac{1}{2\left(-1\right)}\\ x=\frac{1}{2}\end{array}$

Hence the graph is not symmetrical about y axis.

For $y=6x^2+9$:

The axis of symmetry is:

$\begin{array}{l}x=-\frac{b}{2a}\\ x=-\frac{0}{2\left(6\right)}\\ x=0\end{array}$

Hence the graph is symmetrical about y axis.

For $y=3x^2-3x+1$:

The axis of symmetry is:

$\begin{array}{l}x=-\frac{b}{2a}\\ x=-\frac{\left(-3\right)}{2\left(3\right)}\\ x=\frac{1}{2}\end{array}$

Hence the graph is not symmetrical about y axis.

Step 3. Conclusion.

Among the given equations, the graph which is symmetrical about the y-axis is

$y=6x^2+9$.