Question

The vertex of this parabola is at 2, -1 When the y-value is 0 the x value is 5 what is the coefficient of the squared term in the parabola equation.

A. -3
B. -4
C. 4
D. 3

Answer 1

Fot this parabola the coefficient for squared term is 7

Explanation:

The formula for vertex equation is:

x = a*(y-h)^{2}+kx=a∗(y−h)

2

+k

if vertex is at (-3,-1) and in the formula the vertex is (k,h), we replace this values

x = a*(y +1)^{2} -3x=a∗(y+1)

2

−3

The other point of this parabola is (4,0), so we replace it in the formula below:

4 = a*(0 + 1)^{2} -34=a∗(0+1)

2

−3

4 = a*(1)-34=a∗(1)−3

4 +3= a*(1)4+3=a∗(1)

a=7a=7

Answer 2

`\large \boxed{\sf (1)/(9)}`

Explanation:

`\sf y=a(x-h)^2+k`

`\sf Vertex = (h,k)`

y-value is 0 and the x value is 5

h = 2

k = -1

`\sf 0=a(5-2)^2+-1`

Solve for
`\sf a` (the coefficient of the squared term).

`\sf 0=a(3)^2+-1`

`\sf 0=9a-1`

`\sf 9a=1`

`\displaystyle \sf a=(1)/(9)`

The coefficient of the squared term in the parabola equation is 1/9.