Question

What are the x-intercept(s) of the graph of the equation y − x^2 = −4x − 5?

Answer 1

rewrite the equation

\[y = x^2 -4x - 5\]

to find the x-intercepts let y = 0

then you have

\[0 = x^2 - 4x - 5\]

this quadratic can be factorised

find the factors of -5 that add to -4 the bigger factor is negative and the smaller is positive

Answer 2

(1, 0) and (−5, 0)..

Answer 3

just a bit quick...

-5 and 1 are the essential numbers

so you factorise and get (x -5)(x+1) = 0

now the intercepts will be the same numbers with opposite signs

Answer 4

the reason is that the equation must equal zero

I'll substitute x = 5 into the factorised equation

y = ( 5 -5)(5 +1)

this gives 0 * 6 = 0

same when you subdtitute x = -1

y = (-1 -5)(-1+1)
-6 * 0
y = 0

Answer 5

(−1, 0) and (5, 0)

Answer 6

thats correct...

there are a few tips about factorising and factors

in a quadratic ax^2 + bx + c

if b and c are positive both factors are positive

b negative and c positive both factors are negative

if c is negative 1 factor is negative... b positive the larger factor is positive
b negative the larger factor is negative

hope it all helps