Question 414397
y=x^(2)+6x-7

To find the x-intercept, substitute in 0 for y and solve for x.
(0)=x^(2)+6x-7

Since x is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation.
x^(2)+6x-7=(0)

Remove the parentheses around the expression 0.
x^(2)+6x-7=0

In this problem 7*-1=-7 and 7-1=6, so insert 7 as the right hand term of one factor and -1 as the right-hand term of the other factor.
(x+7)(x-1)=0

Set each of the factors of the left-hand side of the equation equal to 0.
x+7=0_x-1=0

Since 7 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 7 from both sides.
x=-7_x-1=0

Set each of the factors of the left-hand side of the equation equal to 0.
x=-7_x-1=0

Since -1 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 1 to both sides.
x=-7_x=1

The complete solution is the set of the individual solutions.
x=-7,1

To find the y-intercept, substitute in 0 for x and solve for y.
y=(0)^(2)+6(0)-7

Expand the exponent (2) to the expression.
y=(0^(2))+6(0)-7

Squaring a number is the same as multiplying the number by itself (0*0).  In this case, 0 squared is 0.
y=(0)+6(0)-7

Multiply 6 by each term inside the parentheses.
y=0+0-7

Solve the equation.
y=-7

These are the x and y intercepts of the equation y=x^(2)+6x-7.
x=-7,1, y=-7