Question

I need help please hekp

Answer 1

`\displaystyle y=(3)/(2)x^2-9x+(19)/(2)`

Explanation:

Equation of the Quadratic Function

The vertex form of the quadratic function has the following equation:

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

Where (h, k) is the vertex of the parabola that results when plotting the function, and a is a coefficient different from zero.

Substituting the coordinates of the vertex (3,-4):

`y=a(x-3)^2-4`

Now we find the value of a by substituting the point through which the function passes (1,2):

`2=a(1-3)^2-4`

Operating:

`2=4a-4`

`4a=6`

`a=(3)/(2)`

Thus, the equation is:

`\displaystyle y=(3)/(2)(x-3)^2-4`

Expanding the square:

`\displaystyle y=(3)/(2)(x^2-6x+9)-4`

Operating:

`\displaystyle y=(3)/(2)x^2-9x+(27)/(2)-4`

Simplifying:

`\boxed{\displaystyle y=(3)/(2)x^2-9x+(19)/(2)}`