Question

Use complete sentences to explain how you would use graphing technology to find the solutions of 0 = −x2 + 2.5x + 1. What do the solutions of 0 = −x2 + 2.5x + 1 represent on the graph of the equation?

Answer 1

hm what does "graphing technology" mean exactly?

to solve \(f(x)=\text{“some number } a"\) means, find the \(x\)'s such that \(f(x)=a\). On a graph, that means,

find the points (x,y) on the graph that are also on the horizontal line drawn.

Answer 2

it just means like that.

Answer 3

a point of the graph is a point of the form \((x,f(x))\). so if it also on the line \(y=a\), that means that \(f(x)=a\).

the sentence would be: I have to find the x-coordinates of the intersection points of the graph of \(f\) with the line with equation \(y=a\).

Answer 4

so, choose \(a=0\) and this answers the first question.

the interpretation... since the line \(y=0\) is the x-axis, the solutions represent.. the intersection points of the graph of f with the x-axis.