How does the a, h and k variables affect a parabola?
assuming you mean a parabola of the form
y = a(x-h)^2+k
Then the vertex is at (h,k).
The graph is that of y=x^2, but vertically scaled by a factor of a, and shifted right by h and up by k.
As for general quadratics, the question makes no sense.
and how do the same variables affect a quadratic graph?
The variables a, h, and k are used to define the equation of a parabola in standard form, which is given by the equation:
y = a(x - h)^2 + k
In this equation, a determines the stretch or compression of the parabola. If a is positive, the parabola opens upwards, and if it is negative, the parabola opens downwards. The value of a also affects the steepness of the parabola. A larger value of a makes the parabola narrower (more vertically compressed), while a smaller value of a makes the parabola wider (more vertically stretched).
The values of h and k determine the vertex of the parabola. The vertex is the point (h, k) and represents the lowest or highest point on the parabola, depending on its orientation. A positive value of h shifts the parabola horizontally to the right, and a negative value of h shifts it horizontally to the left. Similarly, a positive value of k shifts the parabola vertically upward, while a negative value of k shifts it vertically downward.
In summary, a affects the shape and steepness of the parabola, while h and k affect its position or vertex.