Let's illustrate the problem and solve it step-by-step. We are asked to find the expression for [tex]\( y \)[/tex] as a function of [tex]\( x \)[/tex]:
[tex]\[
y = x^2 + 3x - 4
\][/tex]
### Step-by-Step Solution:
1. Identify the given equation:
The equation provided is already in the standard quadratic form:
[tex]\[
y = x^2 + 3x - 4
\][/tex]
2. Interpret the quadratic expression:
This is a quadratic equation in terms of [tex]\( x \)[/tex], where the coefficient of [tex]\( x^2 \)[/tex] is 1, the coefficient of [tex]\( x \)[/tex] is 3, and the constant term is -4.
3. Confirm the structure:
The form [tex]\( y = ax^2 + bx + c \)[/tex] is identifiable, where:
- [tex]\( a = 1 \)[/tex]
- [tex]\( b = 3 \)[/tex]
- [tex]\( c = -4 \)[/tex]
4. Solution complete:
No further simplification or transformation is needed since the equation given, [tex]\( y = x^2 + 3x - 4 \)[/tex], is already in its simplest form.
Therefore, the solution based on the given expression for [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex] is:
[tex]\[
y = x^2 + 3x - 4
\][/tex]
This completes our detailed examination and presentation of the quadratic equation provided.
