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Desmos: Graph each choice
The choices are written ax² + bx + c = 0.
In Desmos, change the 0 to y.
Type y = ax² + bx + c.
No Real Solutions
No real solutions means the graph does NOT INTERSECT the x-axis.
Example
Which graph has no real solutions?
A. 2x² − 11x + 12 = 0
B. 3x² + x − 4 = 0
C. 2x² + 2x + 3 = 0
D. 2x² + x − 3 = 0
In Desmos, change each 0 to y.
No real solutions means the graph does NOT INTERSECT the x-axis.
The graph of y = 2x² + 2x + 3 does NOT INTERSECT the x-axis.
That equation has no real solutions.
Answer: C. 2x² + 2x + 3 = 0
Together
Work these three in a session. Graph each choice in Desmos.
Which graph has no real solutions?
Show Answer
In Desmos, change each 0 to y.
No real solutions means the graph does NOT INTERSECT the x-axis.
The graph of y = 3x² − 2x + 2 does NOT INTERSECT the x-axis.
That equation has no real solutions.
Answer: A. 3x² − 2x + 2 = 0
Which graph has no real solutions?
Show Answer
In Desmos, change each 0 to y.
No real solutions means the graph does NOT INTERSECT the x-axis.
The graph of y = 4x² + 4x + 3 does NOT INTERSECT the x-axis.
That equation has no real solutions.
Answer: D. 4x² + 4x + 3 = 0
Which graph has no real solutions?
Show Answer
In Desmos, change each 0 to y.
No real solutions means the graph does NOT INTERSECT the x-axis.
The graph of y = 2x² − 3x + 3 does NOT INTERSECT the x-axis.
That equation has no real solutions.
Answer: B. 2x² − 3x + 3 = 0
Independent Practice
Try these five on your own. Graph each choice in Desmos.
Which graph has no real solutions?
Show Answer
In Desmos, change each 0 to y.
No real solutions means the graph does NOT INTERSECT the x-axis.
The graph of y = 3x² + x + 2 does NOT INTERSECT the x-axis.
That equation has no real solutions.
Answer: C. 3x² + x + 2 = 0
Which graph has no real solutions?
Show Answer
In Desmos, change each 0 to y.
No real solutions means the graph does NOT INTERSECT the x-axis.
The graph of y = 5x² + 4x + 2 does NOT INTERSECT the x-axis.
That equation has no real solutions.
Answer: A. 5x² + 4x + 2 = 0
Which graph has no real solutions?
Show Answer
In Desmos, change each 0 to y.
No real solutions means the graph does NOT INTERSECT the x-axis.
The graph of y = 2x² + 3x + 4 does NOT INTERSECT the x-axis.
That equation has no real solutions.
Answer: D. 2x² + 3x + 4 = 0
Which graph has no real solutions?
Show Answer
In Desmos, change each 0 to y.
No real solutions means the graph does NOT INTERSECT the x-axis.
The graph of y = 4x² − 2x + 2 does NOT INTERSECT the x-axis.
That equation has no real solutions.
Answer: B. 4x² − 2x + 2 = 0
Which graph has no real solutions?
Show Answer
In Desmos, change each 0 to y.
No real solutions means the graph does NOT INTERSECT the x-axis.
The graph of y = 3x² − 4x + 3 does NOT INTERSECT the x-axis.
That equation has no real solutions.
Answer: C. 3x² − 4x + 3 = 0
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