Q69. - Algebra 1

Question

FIND THE ERROR Chase and Jade are finding the axis of symmetry of a parabola. Is either of them, correct? Explain your reasoning.

Step-by-Step Solution

Answer

Yes, Jade is correct.

Step 1. Standard form of quadratic function.

Compare the quadratic function $y=-x^2-4x+6$ with standard form of quadratic function, $y=a{x}^2+bx+c$.

$$\begin{gathered} a=-1 \\ b=-4 \\ c=6 \end{gathered}$$

Step 2. Find the axis of symmetry.

The axis of symmetry is given by $x=-\frac{b}{2a}$. Substitute $-1$ for a, $-4$ for b into $x=-\frac{b}{2a}$.

$$\begin{gathered} x=-\frac{\left(-4\right)}{2\left(-1\right)} \\ =-\frac{4}{2} \\ =-2 \end{gathered}$$

Step 3. Write the conclusion.

The obtained axis of symmetry matches with the axis of symmetry calculated by Jade. Chase forgot the negative sign with 4.

 

Therefore, Jade is correct.