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The axis of symmetry of the graph of a quadratic equation in standard form is the vertical line x = - b2a.
C
We want to select the equation that has a graph that is symmetric about the y-axis. Note that all of the given equations are quadratic equations in standard form.
y= ax^2 + bx+ c
Let's recall the equation of the axis of symmetry of a parabola described by a quadratic equation in this form.
Let's highlight the values of a, b, and c in each of the given equations to see which of them has b = 0.
| Option | Equation | b ? = 0 |
|---|---|---|
| A | y = 1x^2+ 3x +( - 1) | No |
| B | y = - 1x^2+ 1x+ 0 | No |
| C | y= 6x^2 + 0x + 9 | Yes |
| D | y = 3x^2 +( - 3)x + 1 | No |
The only equation which has b equal to 0, and subsequently is symmetric about the y-axis, is option C.