Question

What is "vertex (2,1)​, point (1, -5)" in vertex form?

Answer 1

Also could someone show me how to write it in vertex form, please?

Answer 2

If the vertex is (h, k), then the form of the equation you want is

y = a(x - h)^2 + k , so for your information with a vertex of (2,1) you have
y = a(x - 2)^2 + 1
so the only missing part is the value of a
but you also know that the point (1, -5) lies on your parabola, so ....
-5 = a(1-2)^2 + 1
-6 = -a
a = 6

equation : y = 6(x - 2)^2 + 1

Answer 3

that should have been

a = -6
and
y = -6(x - 2)^2 + 1

Answer 4

[AI-generated answer — Explain Bot]

To express the equation of a quadratic function in vertex form, we use the formula:

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

Where (h, k) represents the coordinates of the vertex. In this case, we are given the vertex (2, 1). So, the equation in vertex form will have the form:

y = a(x-2)^2 + 1

To find the value of 'a', we need an additional point. Fortunately, we are given the point (1, -5). We can substitute these values into the equation to solve for 'a'.

-5 = a(1-2)^2 + 1
-5 = a(-1)^2 + 1
-5 = a + 1

Now, we can isolate 'a' by subtracting 1 from both sides of the equation:

-5 - 1 = a
-6 = a

So, our equation in vertex form becomes:

y = -6(x-2)^2 + 1

Hence, the equation in vertex form is y = -6(x-2)^2 + 1.