CPM Homework Help : INT2 Problem 9-140

Use any algebraic solution method to calculate the point(s) of intersection for the system given below, if any exist. Explain what your solution indicates about the graph of the system.

$y = x^2 - 4x + 5$
$y = -x^2 + 4x - 1$

$y = x^2 - x - 2$
$y = x^2 + 2x + 1$

Hint 1(a):

Use the equal values (substitution) method.

Hint 2(a):

Solve $x^2 - 4x + 5 = -x^2 + 4x - 1$

Hint 3(a):

Use factoring and the zero product property.

Partial Answer (a):

One point of intersection is $(1, 2)$ .

Hint 1(b):

Use the equal values (substitution) method.

Answer (b):

$(-1, 0)$ is the one point of intersection.