Solve each equation by graphing the related function. If the equation has no real-number solution, write no solution. x^2+7=0
Can someone explain why the answer is no solution?
It is a quadratic.
If the quadratic was y=x^2, that graph would hit (0,0).
Your graph looks like that BUT is 7 units up on the y-axis. Thus it does not hit the x-axis, thus it has no zeros, thus it has no solution : )
thank you so much!
To solve the equation x^2 + 7 = 0 by graphing, we need to first graph the related function y = x^2 + 7.
When we graph y = x^2 + 7, we get a parabola that opens upward, and its vertex is at the point (0, 7). Since the equation x^2 + 7 = 0 means that y = 0, we are looking for the x-values where the graph of y = x^2 + 7 intersects the x-axis.
However, when we look at the graph of y = x^2 + 7, we can see that the entire parabola lies above the x-axis. This means that there are no x-values for which y = x^2 + 7 is equal to zero (no x-intercepts), resulting in no real-number solution.
In conclusion, the equation x^2 + 7 = 0 has no real-number solution because the graph of y = x^2 + 7 does not intersect the x-axis.
To solve the equation x^2 + 7 = 0 by graphing the related function, you need to graph the function y = x^2 + 7 first.
When you graph this function, you will notice that the graph is a parabola that opens upward and has its vertex above the x-axis. Since the parabola never intersects or touches the x-axis, it means that there are no x-values that make y equal to zero. In other words, there are no real solutions to the equation x^2 + 7 = 0.
Visually, the graph will appear as a parabola that is shifted upward by 7 units. Despite shifting the graph, it will never touch or cross the x-axis. Hence, there is no point of intersection with the x-axis and no real solutions exist.
So, the answer to the equation x^2 + 7 = 0 is "no solution."