Question

Passes through (1,12) and has a vertex (10,-4)

Answer 1

To find the equation of a parabola passing through the point (1,12) and having a vertex at (10,-4), we can use the vertex form of a parabola equation.

Step-by-step explanation:

The subject of this question is Mathematics. The question asks to find an equation of a parabola that passes through the point (1,12) and has a vertex at (10,-4).

Let's use the vertex form of a parabola equation, which is y = a(x - h)² + k, where (h,k) is the vertex of the parabola.

Substituting the given values, we have y = a(x - 10)² - 4. Now, we can plug in the coordinates (1,12) to find the value of 'a'. We get 12 = a(1 - 10)² - 4.

Simplifying this equation, we find that 'a' is equal to -1/9. Therefore, the equation of the parabola is y = -1/9(x - 10)² - 4.

Answer 2

Answer: 16/81 (x-10)^2 -4

Step-by-step explanation:

To write a vertex equation with just a point and the vertex, you have to figure out the variables.

In vertex form, the equation is y = a (x-h)^2 + k

Your y is 12, x = 1, h = 10, and k = -4

Plug everything into equation

12 = a (1 - 10)^2 -4

12 = a (-9)^2 - 4

12 = 81a - 4

16 = 81a

16/81 = a

Now you know what the 'a' value is.

If you graph 16/81 (x-10)^2 -4 , you will get a point at (1,12) and a vertex of (10,-4)!

I hope this helps!