Question

Which system of equations does this graph represent?

1) y=x^2-5
y=-x+1

2) y=x^2-5

y=-x-1

3) y=x^2+5
y=-x+1

4) y=x^2+5
y=-x-1
​

Answer 1

1

Explanation:

First, we can find the equation of the parabola. The standard form of a parabola is ax^2 + bx + c,

where c is the y-intercept. The y-intercept on the graph is -5, and every option starts with x^2, so the equation must be x^2 - 5. This rules out options 3 and 4.

Next, we can find the equation of the line. The options are all given in slope-intercept form: y = mx + b, where b is the y-intercept. The y-intercept on the graph is 1, and option 1 has 1 in the place of b. Therefore, option 1 is the answer.