Question

** WILL FAN AND MEDAL **
Write the equation in standard form for the quadratic function that has each set of characteristics
a) Zeros at x=0 and x=-7; contains the point (-2,-5)
b) One zero at x=-3/2, vertex at (1,25)

Answer 1

clue:
standard quadratic form
\[y=Ax^2+Bx+C\]
A,B,C are the unknowns you need to find

Answer 2

do i need to use the equation y=a(x-r)(x-s) ?

Answer 3

where 0 is R, -7 is S, -2 is X and -5 is Y?

Answer 4

the equation i have given and the one you have written are acutally the same thing, but lets just work with yours for now,

you need to understand that 'x' and 'y' are not unknowns, 'y' is just a function of 'x'

the question is asking you to find r,s,a

Answer 5

okay well how do you find the variables?

Answer 6

you were right about r=0 and s=-7
so, substitute them in your equation, what do you get?

Answer 7

y=a(x-r)(x-s)
0=r -7=s -2=x -5=y
-5=a(-2-0)(-2-(-7))
-5=a(-2)(5)
-5/10a = -10a/-10a
-5/10 simplified = 1/2
factored:
y=1/2(x-0)(x-7)
=1/2(x)(x-7)
standard:
y=1/2(x)(x-7)
=(1/2x)(x-7)
=1/2x^2+7/2

Answer 8

@baru ^

Answer 9

the steps are correct :)
but you have made some algebraic mistakes towards the end
\[y=\frac{1}{2}x^2-\frac{7}{2}x\]

Answer 10

haha oops
i'm confused with part b because i got a fraction and i don't know what to do next

Answer 11

y=a(x-r)(x-5)
25=A(1-(-3/2))(1-(-3/2)

Answer 12

I made -3/2=r , -3/2=s , 1=x and 25=y
@baru

Answer 13

hmm,
you can substitute r=-3/2 and s=-3/2 if they say "both zeroes" are -3/2,
since they haven't: only r=-3/2

do you know what a parabola is?

Answer 14

i don't know an exact definition off the top of my head

Answer 15

but have you learnt it? the equation of a parabola?

Answer 16

yes we've learnt about parabolas.
i don't remember the equation for them

Answer 17

well, the second question mentions "vertex"
vertex here refers to the highest/lowest point the parabola(parabolas are quadratic functions)
A parabola looks like a 'U' (it maybe upside down or rotated sideways..but still a 'U')

from the information given, you can recognize that they are talking about a downward parabola.

so we use the equation for a downward parabola with a shifted vertex.

perhaps you haven't learnt these things, so maybe there's an easier way

Answer 18

in any case, i'll just give you the equation
\[(x-h)^2=-4a(y-k)^2\]

h,k,a are the unknowns

here (h,k) is the vertex, you can substiute (1,25)
and then you can substitute y=0 and x=-3/2 since-3/2 is a zero