Draw the graph of y=x^2-4x-5 and use it to solve the equations.
a)x^2-5x-3
b)x^2-3x-4
This should be a graph of quadratic equation. Range -3 to 5?
Cannot draw a graph on these posts.
To draw the graph of the equation y=x^2-4x-5, you can follow these steps:
1. Determine the x and y values: Choose a range of x values that you think is appropriate to plot on the graph. For example, let's take a range from -5 to 5. Substitute these x values into the equation to find the corresponding y values.
When x = -5:
y = (-5)^2 - 4(-5) - 5 = 25 + 20 - 5 = 40
When x = -4:
y = (-4)^2 - 4(-4) - 5 = 16 + 16 - 5 = 27
Continue this process for other x values within the range.
2. Plot the points: Use a coordinate plane to plot the points (x, y) you found in step 1. For example, when x = -5, y = 40, plot the point (-5, 40).
3. Connect the points: Once you have plotted all the points, connect them to form a smooth curve. This curve represents the graph of the equation y = x^2 - 4x - 5.
Now let's use this graph to solve the given equations:
a) To solve x^2 - 5x - 3 = 0 using the graph, find the x-intercepts or the points where the graph crosses the x-axis. These are the values of x for which y = 0.
On the graph, locate the points where the curve crosses the x-axis (where y = 0), and read the corresponding x-values. These will be the solutions to the equation.
b) Similarly, to solve x^2 - 3x - 4 = 0 using the graph, locate the x-intercepts and read the corresponding x-values as the solutions to the equation.
Note: In the given equation y = x^2 - 4x - 5, the range you mentioned (-3 to 5) refers to the range of x-values you want to consider when plotting the graph, not the range of the function. The range of the function is the set of all possible y-values that the function can output.