The graph has the equation

y = a(x - h)² + k  where the vertex = (h,k)

So it has the equation:

y = a(x - 3)² - 2

But we don't know "a" yet.

Draw the two points



Since the vertex is (3,-2), we draw the axis of symmetry
as a vertical line through the vertex:



We can draw the graph approximately:



So you see the x-intercepts are somewhere around 1 and a half and
4 and a half.  But that won't do.  We have to get them to the nearest
hundredth.

Since the graph passes through (0,7), the y-intercept, we substitute
that point in:

y = a(x - 3)² - 2

7 = a(0 - 3)² - 2

7 = a(-3)² - 2

7 = a(9) - 2

7 = 9a - 2

9 = 9a

1 = a

So the equation is

y = 1(x - 3)² - 2

y = (x - 3)² - 2

y = (x - 3)(x - 3) - 2

y = x² - 6x + 9 - 2

y = x² - 6x + 7

To find the x-intercepts, substitute 0 for y

0 = x² - 6x + 7

x² - 6x + 7 = 0



















Using the -, 1.585786438

Using the +, 4.414213562

To the nearest hundredth, the solutions are 1.59 and 4.41

So those two points where the parabola crosses the x-axis

are  (1.59,0) and (4.41,0).

So you write your answer (1.59,0), (4.41,0).

Edwin