Solve the equation x^2 + 14x -49 = 0 by graphing the related function.
the answer is c because if 14x-49 is equivalent then the answer would be c so the answer is d
there are many handy online graphing sites.
Or graph it by hand as usual
To graph the related function, we will first rewrite the equation in the form of a quadratic function: f(x) = x^2 + 14x - 49.
To graph this function, we can use the standard form of a quadratic function, which is f(x) = ax^2 + bx + c. Comparing this standard form with our quadratic function, we have a = 1, b = 14, and c = -49.
Now, let's plot the graph by following these steps:
1. Determine the x-intercepts (or roots) of the quadratic function by setting f(x) = 0.
Set x^2 + 14x - 49 = 0, and solve for x.
Using factoring or the quadratic formula, we can find the roots.
By factoring:
(x + 7)(x - 7) = 0
x + 7 = 0 or x - 7 = 0
x = -7 or x = 7
Therefore, the x-intercepts (or roots) are x = -7 and x = 7.
2. Determine the y-intercept by evaluating f(0).
Substitute x = 0 into the function:
f(0) = 0^2 + 14(0) - 49
f(0) = -49
Therefore, the y-intercept is y = -49.
3. Plot the x-intercepts (-7, 0) and (7, 0), as well as the y-intercept (0, -49), on the coordinate plane.
Now, let's draw the graph that passes through these points and has a parabolic shape.
The graph of the function y = x^2 + 14x - 49 will look like this:
|
-50| *
|
-40 |
|
-30 |
|
-20 |
|
-10 | *
|
0+--------------------*
| |
-10 10
Using the graph, you can visually see where the function crosses the x-axis (x-intercepts) and the y-axis (y-intercept). The x-intercepts are x = -7 and x = 7, and the y-intercept is y = -49.
Therefore, the solutions to the equation x^2 + 14x - 49 = 0 are x = -7 and x = 7.
To solve the equation x^2 + 14x - 49 = 0 by graphing the related function, you need to follow these steps:
1. Rearrange the equation: x^2 + 14x - 49 = 0. This is a quadratic equation in the form of ax^2 + bx + c = 0, where a = 1, b = 14, and c = -49.
2. Graph the quadratic function: To graph the function, you can use any graphing tool or software like Desmos or graph paper. The equation is already in the form y = ax^2 + bx + c, so you can plot points on the coordinate plane.
3. Locate the x-intercepts: The x-intercepts of the graph represent the solutions to the equation. These are the points where the graph intersects the x-axis. In other words, they are the values of x where y equals zero.
4. Find the solutions: The solutions are the x-values of the x-intercepts. These are the values of x where the graph intersects the x-axis. In other words, they are the values that make y equal to zero.
By following these steps, you can solve the equation x^2 + 14x - 49 = 0 by graphing the related function.