Question

PLEASE ANSWER!!!!!!!! Which system of equations does this graph represent? Linear graph and parabola. They intersect at 2, negative 1 and negative 3, 4 (1 point)

A. y = x2 − 5 y = −x + 1
B. y = x2 − 5 y = −x − 1
C. y = x2 + 5 y = −x + 1
D. y = x2 + 5 y = −x − 1

Answer 1

Option (A)

Explanation:

For equation of the line,

Let the equation is, y = mx + b

Slope 'm' of the line passing through two points (-3, 4) and (2, -1),

m =
`(y_2-y_1)/(x_2-x_1)`

=
`(4+1)/(-3-2)`

= -1

y-intercept of this line, b = 1

Now we substitute these values in the equation,

y = -x + 1

Let the equation of the parabola is,

y = a(x - h)² + k

Here, (h, k) is the vertex of the parabola,

Since vertex of the given parabola is (0, -5),

then the equation will be,

y = a(x - 0)²- 5

y = ax² - 5

Since a point (2, -1) lies on this parabola,

-1 = a(2)² - 5

5 - 1 = 4a

a = 1

Equation of the parabola will be,

y = x² - 5

Therefore, Option (A) will be the answer.