Asked by y912f

can you please show me in steps how to find f(1+a)
in this equation
f(x)=-2x^2+4x+6
i know that you will plug in 1+a anywhere there is x. but after that i get confused.

also can you tell me how to find the domain and range of a relation
for ex. 2x+5y=10
thanks for your help!
Answered by Reiny
f(x)=-2x^2+4x+6
f(1+a) = -2(1+a)^2 + 4(1+a) + 6
= -2(1 + 2a + a^2) + 4 + 4a + 6
= -2 -4a -2a^2 + 10 + 4a
= -2a^2 + 8

for 2x+5y=10 both the domain and range are the real numbers
You are looking at a slanted line, (slope=-2/5), so you will find the graph for whatever x you use, and for whatever y you use.
This is true for all straight line graphs, which are neither vertical nor horizontal.
Answered by Reiny
btw, why are you calling this "trig" ?
Answered by y912f
ok,thanks alot.. what about this one : y=2x^2-5

Answered by y912f
its in the first chapter of my trig course. i know its review frm geometry and alg
Answered by Reiny
this is a vertical parabola, meaning it opens either upwards or downwards

the domain of any vertical parabola is the set of real numbers

for the range:
if the parabola opens up, then y ≥ the y value of the vertex
if the parabola opens down, then y ≤ the y value of the vertex

in this case
Domain : x any real number
Range : y ≥ -5, y being real
Answered by y912f
ok. so do u mean that to figure this out u always have to graph the relation?
Answered by Reiny
no, you just have to find the vertex.

Here is a quick way to find the vertex:

if y = ax^2 + bx + c

then the x of the vertex is -b/(2a)
sub that back into the function to find the y value.
Answered by y912f
im sry im still kinda confused. can you show me once again please and explain everything you do thnks:
y=2x+3

y=4/square root of x^2+81

thnks alot!!
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