how do you find the vretex and y-intercept of y=2(x-13)^2-50?

Question

i need someone to walk me through how to find
a) the vertex
b) the y-intercept
y=2(x-13)^2-50

thank you!

Answer 1

y = 2(x - 13)^2 - 50

a) The general formula for a parabola in vertex form is

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

Where, (h, k) are the coordinates of the vertex. In the parabola above, it is obvious that h = 13, and k = -50, so this means our vertex is located at (13, -50).

b) To find the y-intercept, we make x equal to 0. After all, this is the very definition of a y-intercept; where x = 0. (As a side note, if we wanted the x-intercepts, we'd make y = 0).

y = 2(x - 13)^2 - 50

Making x = 0, we have

y = 2(0 - 13)^2 - 50
y = 2(-13)^2 - 50
y = 2(169) - 50
y = 338 - 50
y = 288

So the y-intercept is 288; more specifically, the curve crosses at the point (0, 288).

Answer 2

this equation is already in y=(x-h)^2-k form so u can find the vertex just by looking at it its at (13, -50)

and for y intercept you just sub in 0 for x and solve
and you get y= 288