Use graphing to find the solutions to the system of equations.
enlarged left-brace Start Layout 1st row x squared minus y equals 4 2nd row 2 x plus y equals negative 1 End Layout
(1 point)
Responses
A line and a quadratic function are graphed on a coordinate plane.
A quadratic function goes through the points left parenthesis negative 3 comma 5 right parenthesis and left parenthesis 3 comma 5 right parenthesis. The vertex is at left parenthesis 0 comma negative 4 right parenthesis.
The line goes through the points left parenthesis negative 3 comma negative 7 right parenthesis and left parenthesis 3 comma 5 right parenthesis.
The line and quadratic function intersect at the points left parenthesis negative 1 comma negative 3 right parenthesis and left parenthesis 3 comma 5 right parenthesis.
Image with alt text: A line and a quadratic function are graphed on a coordinate plane. A quadratic function goes through the points left parenthesis negative 3 comma 5 right parenthesis and left parenthesis 3 comma 5 right parenthesis. The vertex is at left parenthesis 0 comma negative 4 right parenthesis. The line goes through the points left parenthesis negative 3 comma negative 7 right parenthesis and left parenthesis 3 comma 5 right parenthesis. The line and quadratic function intersect at the points left parenthesis negative 1 comma negative 3 right parenthesis and left parenthesis 3 comma 5 right parenthesis.
A line and a quadratic function are graphed on a coordinate plane.
A quadratic function goes through the points left parenthesis negative 3 comma 5 right parenthesis and left parenthesis 3 comma 5 right parenthesis. The vertex is at left parenthesis 0 comma negative 4 right parenthesis.
The line goes through the points left parenthesis negative 3 comma 5 right parenthesis and left parenthesis 3 comma negative 7 right parenthesis.
The line and quadratic function intersect at the points left parenthesis negative 3 comma 5 right parenthesis and left parenthesis 1 comma negative 3 right parenthesis.
Image with alt text: A line and a quadratic function are graphed on a coordinate plane. A quadratic function goes through the points left parenthesis negative 3 comma 5 right parenthesis and left parenthesis 3 comma 5 right parenthesis. The vertex is at left parenthesis 0 comma negative 4 right parenthesis. The line goes through the points left parenthesis negative 3 comma 5 right parenthesis and left parenthesis 3 comma negative 7 right parenthesis. The line and quadratic function intersect at the points left parenthesis negative 3 comma 5 right parenthesis and left parenthesis 1 comma negative 3 right parenthesis.
A line and a quadratic function are graphed on a coordinate plane.
A quadratic function goes through the points left parenthesis negative 3 comma negative 5 right parenthesis and left parenthesis 3 comma negative 5 right parenthesis. The vertex is at left parenthesis 0 comma 4 right parenthesis.
The line goes through the points left parenthesis negative 3 comma 5 right parenthesis and left parenthesis 3 comma negative 7 right parenthesis.
The line and quadratic function intersect at the points left parenthesis negative 1.5 comma 2 right parenthesis and left parenthesis 3.5 comma negative 8 right parenthesis.
Image with alt text: A line and a quadratic function are graphed on a coordinate plane. A quadratic function goes through the points left parenthesis negative 3 comma negative 5 right parenthesis and left parenthesis 3 comma negative 5 right parenthesis. The vertex is at left parenthesis 0 comma 4 right parenthesis. The line goes through the points left parenthesis negative 3 comma 5 right parenthesis and left parenthesis 3 comma negative 7 right parenthesis. The line and quadratic function intersect at the points left parenthesis negative 1.5 comma 2 right parenthesis and left parenthesis 3.5 comma negative 8 right parenthesis.
A line and a quadratic function are graphed on a coordinate plane.
A quadratic function goes through the points (-3, 5) and (3, 5), with the vertex at (0, -4). The line goes through the points (-3, -7) and (3, 5). The line and quadratic function intersect at the points (-1, -3) and (3, 5).
To find the solutions to the system of equations, we can graph the equations and find the points of intersection.
The system of equations is:
1) x^2 - y = 4
2) 2x + y = -1
Let's start by graphing the first equation, x^2 - y = 4:
The quadratic function goes through the points (-3, 5) and (3, 5), and the vertex is at (0, -4).
Next, let's graph the second equation, 2x + y = -1:
The line goes through the points (-3, -7) and (3, 5).
Now, we can see that the line and quadratic function intersect at the points (-1, -3) and (3, 5).
Therefore, the solutions to the system of equations are (-1, -3) and (3, 5).
To find the solutions to the system of equations using graphing, you need to graph both equations on a coordinate plane and see where they intersect.
The first equation is x^2 - y = 4, which represents a quadratic function. To graph this, you can plot a few points or use the vertex form. Since the vertex is given, which is (0, -4), you can plot this point on the graph. Then you can use symmetry to plot two more points on each side of the vertex. For example, if (0, -4) is the vertex, then (-3, 5) and (3, 5) would be on the graph. Connect these points to get the graph of the quadratic function.
The second equation is 2x + y = -1, which represents a line. To graph this, you can plot a few points or use the slope-intercept form. Rearrange the equation to y = -2x - 1, which tells you that the y-intercept is -1 and the slope is -2. Plot the y-intercept, which is (0, -1), and use the slope to find additional points. For example, if the slope is -2, then if you move one unit to the right and two units down from the y-intercept, you will get the point (1, -3). Connect these points to get the graph of the line.
Now, look at the graph and see where the line and quadratic function intersect. Those points of intersection are the solutions to the system of equations. In this case, it appears that the line and quadratic function intersect at the points (-1, -3) and (3, 5).
So, the correct response would be: "The line and quadratic function intersect at the points (-1, -3) and (3, 5)."