Sure, let's identify the properties of the given quadratic equation:
[tex]\[ y = -3x^2 + 6x + 17 \][/tex]
### Step-by-Step Solution:
1. Identifying the coefficients:
The general form of a quadratic equation is:
[tex]\[ y = ax^2 + bx + c \][/tex]
By comparing the given quadratic equation [tex]\( y = -3x^2 + 6x + 17 \)[/tex] with the general form, we can identify the coefficients [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex].
2. Coefficients:
- [tex]\( a \)[/tex] is the coefficient of [tex]\( x^2 \)[/tex].
- [tex]\( b \)[/tex] is the coefficient of [tex]\( x \)[/tex].
- [tex]\( c \)[/tex] is the constant term.
Therefore, from the given quadratic equation:
- [tex]\( a = -3 \)[/tex]
- [tex]\( b = 6 \)[/tex]
- [tex]\( c = 17 \)[/tex]
### Summary:
[tex]\[
\begin{aligned}
a: & \, -3\\
b: & \, 6\\
c: & \, 17
\end{aligned}
\][/tex]
So, the coefficients of the quadratic equation [tex]\( y = -3x^2 + 6x + 17 \)[/tex] are:
[tex]\[
a = -3,\ b = 6,\ c = 17
\][/tex]
