To find the expression for [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex] in the given quadratic equation, let's break down the process step-by-step:
1. Identify the Form of a Quadratic Equation:
A quadratic equation generally takes the form:
[tex]\[
y = ax^2 + bx + c
\][/tex]
where [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex] are constants.
2. Given Equation:
In this specific case, the given quadratic equation is:
[tex]\[
y = x^2 + 8x + 15
\][/tex]
3. Coefficients of the Equation:
Comparing with the general form [tex]\( y = ax^2 + bx + c \)[/tex]:
- [tex]\( a = 1 \)[/tex] (coefficient of [tex]\(x^2\)[/tex])
- [tex]\( b = 8 \)[/tex] (coefficient of [tex]\(x\)[/tex])
- [tex]\( c = 15 \)[/tex] (constant term)
4. Construct the Quadratic Expression:
Putting it all together, the quadratic expression in the equation is:
[tex]\[
y = x^2 + 8x + 15
\][/tex]
This equation tells us how [tex]\( y \)[/tex] changes with respect to [tex]\( x \)[/tex]. Solutions or roots of this quadratic equation can be found by factoring, completing the square, or using the quadratic formula, but those are additional steps depending on the specific problem requirements.
So, the quadratic equation for [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex] is:
[tex]\[
y = x^2 + 8x + 15
\][/tex]
