Question

I need help please hekp

Answer 1

Answer:

$\displaystyle y=\frac{3}{2}x^2-9x+\frac{19}{2}$

Step-by-step 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:

$2=4a-4$

$4a=6$

$a=\frac{3}{2}$

Thus, the equation is:

$\displaystyle y=\frac{3}{2}(x-3)^2-4$

Expanding the square:

$\displaystyle y=\frac{3}{2}(x^2-6x+9)-4$

Operating:

$\displaystyle y=\frac{3}{2}x^2-9x+\frac{27}{2}-4$

Simplifying:

$\boxed{\displaystyle y=\frac{3}{2}x^2-9x+\frac{19}{2}}$