Question

Find the equation of the parabola if vertex at (2, 5), axis parallel to the x-axis, passing through (0, 4)

Answer 1

@jim_thompson5910 help please :)

Answer 2

how far did you get

Answer 3

not far at all...
do we use the equation y = (x - h)2 + k

Answer 4

that's if the line of symmetry is parallel to the y axis

Answer 5

or there is anothe one we learnt at school which is (y-k)^2 = 4a(x-h)

Answer 6

that's the one we'll use

Answer 7

the vertex is (2,5), so

h = 2
k = 5

plug those values in

Answer 8

(y-5)^2 = 4a(x-2)

Answer 9

you also know that (0,4) is on the parabola

so plug x = 0 and y = 4 in as well

Answer 10

then solve for 'a'

Answer 11

a = 1/8

Answer 12

close

Answer 13

negative? a = -1/8

Answer 14

yes

Answer 15

since a = -1/8, this means 4a = 4(-1/8) = -4/8 = -1/2

Answer 16

so

(y-5)^2 = 4a(x-2)

becomes

(y-5)^2 = -1/2(x-2)

Answer 17

Thanks again @jim_thompson5910 :)

Answer 18

you're welcome