Solving Equations Using Graphs Flashcards

All 4 cards in this deck

What are the steps to solve a related equation by drawing a straight line on a given curve?

e.g. use the graph of $y = x^2 + x - 4$ to solve $x^2 + x - 6 = 0$

1. Rearrange so one side matches the curve: $x^2 + x - 4 = 2$
2. Draw the line $y = 2$ on the same axes
3. Read the $x$-coordinates where the line meets the curve.

How do you use a drawn curve to estimate the value of $f(a)$?

e.g. estimate $f(1.5)$

Go up from $x = 1.5$ on the $x$-axis to the curve, then straight across to the $y$-axis and read off the value.

True or false? Solutions found from a graph should be written as coordinates.

False.
Give the $x$-values only, e.g. $0.8$ and $5.2$.

True or false? If the line $y = k$ does not meet the curve $y = f(x)$, then $f(x) = k$ has no solutions in that range.

True.
Solutions correspond to points of intersection of the line and the curve.