To find the solutions to the equation, we need to graph the function f(x) = x^2 - 5x + 4 and find the x-intercepts.
To graph the function, we can use the vertex form of a parabola: f(x) = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.
In this case, the equation x^2 - 5x + 4 can be rewritten as (x - 2.5)^2 - 6.25.
The vertex of the parabola is (2.5, -6.25).
Now, let's find the x-intercepts by setting f(x) = 0.
0 = (x - 2.5)^2 - 6.25
Simplifying, we get:
(x - 2.5)^2 = 6.25
Taking the square root:
x - 2.5 = ±√6.25
x - 2.5 = ±2.5
Solving for x, we have two solutions:
x - 2.5 = 2.5 or x - 2.5 = -2.5
x = 5 or x = 0
Therefore, the solutions to the equation x^2 - 5x = -4 are x = 0 and x = 5.
The graph of the function is a parabola that opens upward and crosses the x-axis at x = 0 and x = 5.
Graph:
Create a function graph to answer the question. What are the solutions to the equation x2−5x=−4
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