Math help Please

Question

The shape of the arches on a bridge form a parabola, given by the equation

where h is height, and x is horizontal distance, both in metres.

h= -9/200x^2 + 9/5x

Use common factoring to help you sketch the graph, showing the coordinates of the x-intercepts

Answer 1

h = (-9/200)x^2 + (9/5)x

h= (-9/200)(x^2 -40x)

h=(-9/200)(x)(x-40) in x intercept form

x intercepts are x= 0 and x =40

y intercept = 0

axis of symmetry is x =20

it's a downward opening parabola with vertex = (20, 18)

take half of 40, square it, multiply by -9/200, then add and subtract

y = h = (-9/200)(x^2 -40x + 400) -(-9/200)400

y coordinate of vertex = (9/200)400 = 18

h= (-9/200)(x-20)^2 +18 in vertex form

the negative sign for the coefficient of the x^2 term means it's downward opening. Since it has x intercepts, that means the vertex is above the x axis and has a y value >0

Plot the vertex and x intercepts, the points (20, 18), (0,0) and (0,40)

and draw a parabolic curve through them, top of the parabola at (20,18) and extending downward through the two intercepts, endlessly downward. Maybe put an arrow at the ends to indicate it goes forever. Except this is a bridge arch, so stop the graph at the x intercepts.