Answer:
The coefficient is 3.
Step-by-step explanation:
The parabola has the vertex at (2,-1).
So, the equation of the parabola in vertex form will be (if its axis of symmetry is parallel to the positive x-axis)
(y + 1)² = 4a(x - 2) ........... (1)
Now, the point (5,0) will satisfy the above equation.
Hence, 1 = 4a(5 - 2) = 12a
⇒ [tex]a = \frac{1}{12}[/tex]
So, from equation (1) we get,
[tex](y + 1)^{2} = 4 \times \frac{1}{12}(x - 2) = \frac{1}{3}(x - 2)[/tex]
⇒ 3(y + 1)² = (x - 2)
⇒ 3y² + 6y + 3 = x - 2
⇒ 3y² + 6y + 5 = x
Therefore, the coefficient of the squared term i.e. y² in the above parabola equation is 3. (Answer)
