Find the equation of the axis of symmetry of the following parabola algebraically.

Question

y, equals, minus, 2, x, squared, plus, 8, x, plus, 6
y=−2x
2
+8x+6

Answer 1

To find the equation of the axis of symmetry for the given parabola represented by the equation $y=-2x^2+8x+6$, we can use the formula for the axis of symmetry for a quadratic function of the form $y=a{x}^2+bx+c$. The formula for the axis of symmetry is given by:

$$x=-\frac{b}{2a}$$

In the given equation, we identify the coefficients:

• $a=-2$
• $b=8$
• $c=6$ (we won't use this for the axis of symmetry calculation).

Now, we substitute the values of $a$ and $b$ into the formula:

$$x=-\frac{8}{2\cdot -2}$$

Calculating the denominator:

$$2\cdot -2=-4$$

Now, substituting this back into the equation gives:

$$x=-\frac{8}{-4}$$ $$x=2$$

Thus, the equation of the axis of symmetry for the parabola is:

$$x=2$$