Sure! To find the axis of symmetry for the given quadratic equation [tex]\(y = 3x^2 + 24x + 42\)[/tex], we can follow these steps:
1. A quadratic equation in the standard form is given by [tex]\(y = ax^2 + bx + c\)[/tex]. In this case, we have:
[tex]\[
a = 3, \quad b = 24, \quad \text{and} \quad c = 42
\][/tex]
2. The formula to determine the axis of symmetry for a quadratic equation is:
[tex]\[
x = -\frac{b}{2a}
\][/tex]
3. Substitute the values of [tex]\(a\)[/tex] and [tex]\(b\)[/tex] into the formula:
[tex]\[
x = -\frac{24}{2 \cdot 3}
\][/tex]
4. Perform the arithmetic operations inside the fraction:
[tex]\[
x = -\frac{24}{6}
\][/tex]
5. Simplify the fraction:
[tex]\[
x = -4
\][/tex]
So, the equation of the axis of symmetry for the given parabola [tex]\(y = 3x^2 + 24x + 42\)[/tex] is:
[tex]\[
x = -4
\][/tex]
Therefore, the axis of symmetry is [tex]\(x = -4\)[/tex].
