What are the x and y intercepts of the graph y=x^2+7x+12

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

y-intercept is (0,12).

Step-by-step explanation:

x-intercept is a point where the value of y is zero.

y-intercept is a point where the value of x  is zero.

Given equation is :

y=x²+7x+12

put x=0 in given equation to find y-intercept.

y=(0)²+7(0)+12

y= 0+0+12

y= 12

hence, y-intercept is (0,12).

put y=0 in given equation to find x-intercept.

0=x²+7x+12

split the middle term of above equation to make the equation into two groups such that the sum of two numbers should be 7 and their product be 12.

x²+3x+4x+12=0

making two groups and taking common out:

x(x+3)+4(x+3)=0

take (x+3) common,

(x+3)(x+4)=0

x+3=0 or x+4=0

x=-3 or x=-4

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