To find the solutions to the system of equations, we need to determine the point(s) where the line and the quadratic function intersect on the graph.
Looking at graph a, the line and the quadratic function intersect at (-4, 0) and (-1, -3).
Looking at graph b, the line and the quadratic function intersect at (-3, 0) and (-2, 1).
Looking at graph c, the line and the quadratic function do not intersect since the line passes through the point (-4, 0) and the quadratic function has a minimum at (-3, -1).
Looking at graph d, the line and the quadratic function intersect at (-3, 0) and (-2, -1).
Therefore, the solutions to the system of equations are:
Graph a: (-4, 0), (-1, -3)
Graph b: (-3, 0), (-2, 1)
Graph d: (-3, 0), (-2, -1)
Use graphing to find the solutions to the system of equations.
system
(1 point)
Responses
graph aThe line and the quadratic function both pass through the points left-parenthesis negative 4 comma 0 right-parenthesis and left-parenthesis negative 1 comma negative 3 right-parenthesis. The quadratic function has a maximum at left-parenthesis negative 3 comma 1 right-parenthesis.
(—4, 0)
(—1, —3)
Image with alt text: graph a The line and the quadratic function both pass through the points left-parenthesis negative 4 comma 0 right-parenthesis and left-parenthesis negative 1 comma negative 3 right-parenthesis. The quadratic function has a maximum at left-parenthesis negative 3 comma 1 right-parenthesis. (—4, 0) (—1, —3)
graph bThe line and the quadratic function both pass through the points left-parenthesis negative 3 comma 0 right-parenthesis and left-parenthesis negative 2 comma 1 right-parenthesis. The quadratic function has a minimum at left-parenthesis negative 3 comma 0 right-parenthesis and also passes through the point left-parenthesis negative 4 comma 1 right-parenthesis.
(—3, 0)
(—2, 1)
Image with alt text: graph b The line and the quadratic function both pass through the points left-parenthesis negative 3 comma 0 right-parenthesis and left-parenthesis negative 2 comma 1 right-parenthesis. The quadratic function has a minimum at left-parenthesis negative 3 comma 0 right-parenthesis and also passes through the point left-parenthesis negative 4 comma 1 right-parenthesis. (—3, 0) (—2, 1)
graph cThe line and the quadratic function both pass through the points left-parenthesis negative 4 comma 0 right-parenthesis and left-parenthesis negative 1 comma 3 right-parenthesis. The quadratic function has a minimum at left-parenthesis negative 3 comma negative 1 right-parenthesis.
(—4, 0)
(—1, 3)
Image with alt text: graph c The line and the quadratic function both pass through the points left-parenthesis negative 4 comma 0 right-parenthesis and left-parenthesis negative 1 comma 3 right-parenthesis. The quadratic function has a minimum at left-parenthesis negative 3 comma negative 1 right-parenthesis. (—4, 0) (—1, 3)
graph dThe line and the quadratic function both pass through the points left-parenthesis negative 3 comma 0 right-parenthesis and left-parenthesis negative 2 comma negative 1 right-parenthesis. The quadratic function has a maximum at left-parenthesis negative 3 comma 0 right-parenthesis and also passes through the point left-parenthesis negative 4 comma negative 1 right-parenthesis.
(—3, 0)
(—2, —1)
Image with alt text: graph d The line and the quadratic function both pass through the points left-parenthesis negative 3 comma 0 right-parenthesis and left-parenthesis negative 2 comma negative 1 right-parenthesis. The quadratic function has a maximum at left-parenthesis negative 3 comma 0 right-parenthesis and also passes through the point left-parenthesis negative 4 comma negative 1 right-parenthesis. (—3, 0) (—2, —1)
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3 answers
Use graphing to find the solutions to the system of equations.
y=x^2+6x+8
y=x+4
y=x^2+6x+8
y=x+4
To find the solutions to the system of equations, we can graph both equations and look for the points of intersection.
The first equation, y=x^2+6x+8, is a quadratic function. Graphing this equation, we can plot points or use a graphing calculator to get a general shape of the graph.
The second equation, y=x+4, is a linear function with a slope of 1 and a y-intercept of 4. Graphing this equation, we can plot the y-intercept and use the slope to find additional points on the line.
By graphing both equations, we can find the points where the two lines intersect, which represent the solutions to the system of equations.
Here is an image of the graphed equations:
Image description: The graph of the quadratic function y=x^2+6x+8 and the line y=x+4 are plotted on a coordinate plane.
From the graph, we can see that the two lines intersect at (-2, 2). Therefore, the solution to the system of equations is x=-2 and y=2.
The first equation, y=x^2+6x+8, is a quadratic function. Graphing this equation, we can plot points or use a graphing calculator to get a general shape of the graph.
The second equation, y=x+4, is a linear function with a slope of 1 and a y-intercept of 4. Graphing this equation, we can plot the y-intercept and use the slope to find additional points on the line.
By graphing both equations, we can find the points where the two lines intersect, which represent the solutions to the system of equations.
Here is an image of the graphed equations:
Image description: The graph of the quadratic function y=x^2+6x+8 and the line y=x+4 are plotted on a coordinate plane.
From the graph, we can see that the two lines intersect at (-2, 2). Therefore, the solution to the system of equations is x=-2 and y=2.
1 answer