Question

What are the x- and y-intercepts of the graph of y = x2 + 7x + 12? x-intercepts: (−3, 0) and (−4, 0)
y-intercept: (0, 12)

x-intercepts: (−3, 0) and (4, 0)
y-intercept: (0, −12)

x-intercepts: (3, 0) and (4, 0)
y-intercept: (0, −12)

x-intercepts: (3, 0) and (−4, 0)
y-intercept: (0, 12)

Answer 1

y=x^2+7x+12
y-intercept: (0,12)
x-intercepts:(-3,0)(-4,0)
(x+3)(x+4)

Answer 2

Answer:  The correct option is

(A) x-intercepts: (−3, 0) and (−4, 0),

     y-intercept: (0, 12).

Step-by-step explanation:  We are given to find the x-intercept and y-intercepts of the following graph :

$y=x^2+7x+12~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

The x-intercepts of the graph (i) is given by

$y=0\\\\\Rightarrow x^2+7x+12=0\\\\\Rightarrow x^2+4x+3x+12=0\\\\\Rightarrow x(x+4)+3(x+4)=0\\\\\Rightarrow (x+3)(x+4)=0\\\\\Rightarrow x+3=0,~~~~~x+4=0\\\\\Rightarrow x=-3,-4.$

So, the x-intercepts are (-3, 0) and (-4, 0).

And, the y-intercepts pf graph (i) is given by

$x=0\\\\\Rightarrow y=0^2+7\times0+12\\\\\Rightarrow y=12.$

So, the y-intercept is (0, 12).

Thus, the x-intercepts are (-3, 0) and (-4,0). And, y-intercept is (0, 12).

Option (A) is CORRECT.