Sure, let's find the coefficient of the squared term in the given parabola's equation step-by-step.
We are given:
- The vertex of the parabola is at (-4, -1).
- Another point on the parabola is (2, 0).
The standard form of a parabola's equation with its vertex at [tex]\((h, k)\)[/tex] is:
[tex]\[ y = a(x - h)^2 + k \][/tex]
Given:
- [tex]\( h = -4 \)[/tex]
- [tex]\( k = -1 \)[/tex]
We need to use the point (2, 0) to determine the coefficient [tex]\( a \)[/tex].
1. Substitute the point (2, 0) into the equation:
[tex]\[ 0 = a(2 - (-4))^2 - 1 \][/tex]
2. Simplify inside the parentheses:
[tex]\[ 0 = a(2 + 4)^2 - 1 \][/tex]
[tex]\[ 0 = a(6)^2 - 1 \][/tex]
3. Simplify further:
[tex]\[ 0 = 36a - 1 \][/tex]
4. Add 1 to both sides of the equation to isolate the term with [tex]\( a \)[/tex]:
[tex]\[ 1 = 36a \][/tex]
5. Solve for [tex]\( a \)[/tex]:
[tex]\[ a = \frac{1}{36} \][/tex]
Therefore, the coefficient of the squared term [tex]\( a \)[/tex] in the parabola's equation is:
[tex]\[ a = 0.027777777777777776 \][/tex]
So, the coefficient of the squared term in the parabola's equation is approximately [tex]\( 0.0278 \)[/tex].
