x-intercepts for the function y= x^2 + 6x +7?

Question

please do setting out so i learn

Answer 1

x-intercepts are found by setting y = 0.

x^2 + 6x + 7 = 0

Then solve by either using the quadratic formula:
a = 1, b = 6, c = 7

x = [-6 +/- sqrt(36 - 4(1)(7)) / [2(1)]
x = [-6 +/- sqrt(36 - 28)] / 2
x = [-6 +/- sqrt(8)] / 2
x = [-6 +/- sqrt(4*2)] / 2
x = [-6 +/- sqrt(4)*sqrt(2)] / 2
x = [-6 +/- 2*sqrt(2)] / 2
x = -3 +/ sqrt(2) <----exact answers

or completing the square:

x^2 + 6x + 9 = -7 + 9
(x + 3)^2 = 2
x + 3 = +/- sqrt(2)
x = -3 +/- sqrt(2) <----exact answers
x = -1.585786438, -4.414213562 <----approximate answers

Answer 2

One way is to use the formula for the roots
x=((-6+-sqrt(36-28))/2 = -3 +-sqrt(2)
The other is completing the square
x^2+6x+7= (x+3)^2-2 = 0 (x+3)^2=2
x+3=+-sqrt2 and x= -3+-sqrt2

Answer 3

x-intercept means the point where the curve meets the x-axis.
that is y-coordinate is zero.
=> x^2 + 6x + 7 = 0
by solving it we get,
x = -1.585786438 [or] -4.414213562
these are the x-intercepts
i used calculator to solve the equation.

Answer 4

for x intercept, y=0
therefore,
x^2+6x+7=0

here
Coefficient of x^2, a=1,
Coefficient of x, b=6,
Constant, c=7

therefore, by using the formula to solve for x,

x= (-b+sq.root(b^2-4ac))/(2a) and
x= (-b-sq.root(b^2-4ac))/(2a),

we get,
x= -1.585786438
or
x= -4.414213562