Question

HINT: You can graph both equations OR

set them equal to each other and solve
UNIT 1
Given the equations y=x+7 and y=x² +4 at what
point (s) do they intercept? (highlight the
correct answer (s)
A. (0,4)
B.
(-1.303,5.697)
C. (2.303,9.303)
D. (-2,-5)
E. (3,10)

Answer 1

B. (-1.303, 5.697).

Explanation:

To find the points at which the two equations intersect, we need to set the two equations equal to each other and solve for x. This gives us the following:

x + 7 = x^2 + 4

We can then use the quadratic formula to solve for x:

x = (-1 +/- sqrt(1 - 41(-4)))/(2*1)

This simplifies to:

x = (-1 +/- sqrt(17))/2

This means that the two equations intersect at the points (x,y) = (-1 + sqrt(17))/2, (-1 - sqrt(17))/2.

Since the answer choices are given in decimal form, we can approximate these values to get the following points:

(-1 + 4.123)/2 = (-0.877, 3.123)

(-1 - 4.123)/2 = (-1.123, 2.877)

Based on these points, the correct answer is (B) (-1.303, 5.697).