To express the quadratic equation [tex]\( y = -0.6x^2 + 1 \)[/tex] in vertex form, which is represented as [tex]\( y = a(x - h)^2 + k \)[/tex], we need to complete the square. Here’s the step-by-step process:
1. Identify the coefficients: The given equation is [tex]\( y = -0.6x^2 + 1 \)[/tex], so:
[tex]\[
a = -0.6, \quad b = 0, \quad c = 1
\][/tex]
2. Determine [tex]\( h \)[/tex]: For a quadratic equation [tex]\( y = ax^2 + bx + c \)[/tex], the value of [tex]\( h \)[/tex] can be found using the formula:
[tex]\[
h = -\frac{b}{2a}
\][/tex]
Since [tex]\( b = 0 \)[/tex]:
[tex]\[
h = -\frac{0}{2(-0.6)} = 0
\][/tex]
3. Determine [tex]\( k \)[/tex]: To find [tex]\( k \)[/tex], use the formula:
[tex]\[
k = c - \frac{b^2}{4a}
\][/tex]
Given [tex]\( b = 0 \)[/tex]:
[tex]\[
k = 1 - \frac{0^2}{4(-0.6)} = 1
\][/tex]
4. Assemble the vertex form: Substitute [tex]\( a \)[/tex], [tex]\( h \)[/tex], and [tex]\( k \)[/tex] into the vertex form equation:
[tex]\[
y = -0.6(x - 0)^2 + 1
\][/tex]
This simplifies to:
[tex]\[
y = -0.6(x - 0)^2 + 1
\][/tex]
Therefore, the values are:
[tex]\[
a = -0.6
\][/tex]
[tex]\[
h = 0
\][/tex]
[tex]\[
k = 1
\][/tex]
So, in vertex form, the equation is [tex]\( y = -0.6(x - 0)^2 + 1 \)[/tex], and the parameters are:
[tex]\[
a = -0.6, \quad h = 0, \quad k = 1
\][/tex]
