Question

the vertex of this parabola is at (2,-4). when the y-value us -3, the x-value is -3. what is the coefficient of the squared term in the parabolas equation?​

Answer 1

-5

Explanation:

from a p e x

Answer 2

The coefficient of the squared term is 1/25.

Explanation:

We are given that the vertex of a parabola is at (2, -4). We also know that y = -3 when x = -3.

And we want to determine the coefficient of the squared term of the equation.

Since we are given the vertex, we can use the vertex form of the quadratic:

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

Where (h, k) is the vertex and a is the leading coefficient. The leading coefficient is also the coefficient of the squared term, so we simply need to find the value of a.

Since the vertex is at (2, -4), h = 2 and k = -4. Substitute:

`\displaystyle y = a(x-2)^2-4`

y = -3 when x = -3. Solve for a:

`\displaystyle (-3) = a((-3)-2)^2-4`

Simplify:

`\displaystyle 1 = a(-5)^2\Rightarrow a = (1)/(25)`

Therefore, our function in vertex form is:

`\displaystyle f(x) = (1)/(25)\left(x-2)^2-4`

Hence, the coefficient of the squared term is 1/25.