We can write the graph of f(x) = (x - 1)(x + 4) as, "On a coordinate plane, a parabola opens up. It goes through (-4, 0), has a vertex at (-1.5, -6.25), and goes through (1, 0)."
What is a parabola?
A parabola is a plane curve created by a moving point whose distance from a stationary point equals its distance from a fixed-line.
How do we solve the given question?
In the question, we are given an equation of f(x) = (x - 1)(x + 4), and are asked to identify its graph.
The given equation is of a parabola in the intercept form f(x) = a(x - p)(x - q), which opens up if a > 0 and opens down if a < 0, and which has a vertex at the point [tex]\left ( \frac{p+q}{2},f\left ( \frac{p+q}{2} \right ) \right )[/tex] , and passes through the point (p, 0) and (q, 0).
Comparing the equation f(x) = (x - 1)(x + 4) to f(x) = a(x - p)(x - q), we get
a = 1, p = 1, q = -4.
Since, a > 0 (a = 1), we can say that it opens up.
Now, we calculate (p + q)/2 = (1 - 4)/2 = -1.5
f((p + q)/2) = f(1.5) = (-1.5 - 1)(-1.5 + 4) = (-2.5)(2.5) = -6.25.
Thus, the vertex is at point (-1.5, -6.25).
Also, the equation passes through the points (-4, 0) and (1, 0).
∴ We can write the graph of f(x) = (x - 1)(x + 4) as, "On a coordinate plane, a parabola opens up. It goes through (-4, 0), has a vertex at (-1.5, -6.25), and goes through (1, 0)."
Learn more about a Parabola at
https://brainly.com/question/17987697
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