Question

The graph of a quadratic function f has a vertex (-1,-10) and passes through the point (1,2). Which of the following represents f in vertex form?

Answer 1

The quadratic function f in vertex form with vertex (-1,-10) and passing through point (1,2) is f(x) = 3(x + 1)^2 - 10.

Step-by-step explanation:

The equation of a quadratic function in vertex form, which is given by f(x) = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. Given that the vertex is (-1, -10) and the function passes through the point (1, 2), we can substitute these values into the vertex form equation to find the value of the coefficient a. Substituting the vertex into the equation, we have f(x) = a(x + 1)^2 - 10.

Then, using the point (1, 2), we can plug in x = 1 and f(x) = 2 to solve for a. This gives us 2 = a(1 + 1)^2 - 10, which simplifies to 2 = 4a - 10. Solving for a, we get a = 3. Therefore, the equation of the quadratic function in vertex form is f(x) = 3(x + 1)^2 - 10.

Answer 2

(y + 10)² = 72(x + 1)

Step-by-step explanation:

If we assume the vertex of the parabola is (α,β) and the axis is parallel to the positive x-axis, then its equation is given by

(y - β)² = 4a(x - α) ........... (1)

Now, the vertex is (-1,-10).

So, the equation will become (y + 10)² = 4a(x + 1) .......... (2)

Now, (1,2) is a point on the parabola.

So, equation (2) becomes (2 + 10)² = 4a(1 + 1)

⇒ 144 = 8a

⇒ 4a = 72

Therefore, the final equation of the parabola in vertex form will be

(y + 10)² = 72(x + 1) (Answer)