Answer:
The coefficient of the squared expression in the parabola equation is [tex]a=4[/tex]
Step-by-step explanation:
The equation of a parabola in its vertex form is:
[tex]y = a(x-h) ^ 2 + k[/tex]
Where the vertex of the parabola is the point (h, k)
a is the ceoficiente of the term to the square.
We need to find the equation of a parabola that has its vertex in the point:
(-5, -2)
So:
[tex]h = -5\\\\k = -2[/tex]
Therefore the equation is:
[tex]y = a(x - (-5)) ^ 2 -2\\\\y = a(x + 5) ^ 2 -2[/tex]
We know that the point (-4, 2) belongs to this parable. Then we can find the value of a by replacing the point in the equation of the parabola
[tex](2) = a((-4) + 5) ^ 2 -2\\\\2 = a(1) ^ 2 -2\\\\2 = a -2\\\\a = 4[/tex]
Finally the coefficient is a = 4
Answer:
The answer is 4
Step-by-step explanation:
This is the correct answer
