Find an equation of quadratic function the graph passes through A(2,3)B(2,3)and C(1,0) and draw the parabola

Answer 1

Since points A and B have the same coordinates, it means they lie on the vertex of the parabola. Therefore, the axis of symmetry is x=2.

Let's write the equation of the parabola in vertex form:

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

where (h,k) is the vertex. Since the axis of symmetry is x=2, we know that h=2. Also, since the parabola passes through C(1,0), we can plug in x=1 and y=0 to get an equation we can solve for a:

0 = a(1 - 2)^2 + 3
0 = a(1) + 3
a = -3

So the equation of the parabola is:

f(x) = -3(x - 2)^2 + 3

To draw the parabola, we can plot the vertex first (2,3), then use the shape of the parabola to plot a few more points. Since a is negative, the parabola opens downwards. Here's the graph: