Graphing method to solve?

Question

How do I solve this equation by the graphing method 12= (x+3)^2 - 2

Please help step by step i don't know what the graphing method is?

Answer 1

Whenever a quadratic equation (one with ^2 in it) is "solved", it is asking for zeros...also known as "the places where the graph crosses the x-axis". To do this, since you are looking for a zero, the equation must equal zero:

12 = (x+3)^2 - 2

Subtract 12 from both sides:

0 = (x+3)^2 - 14

This equation equals zero, and it is in "vertex form". It is a nice, boring parabola, except it has been moved around.

You are looking for the points that show where the graph crosses the x-axis, and your answer will be in the form (?, 0), (?, 0).

To graph it, you have two options...

Temporarily change the 0 to y, set up a t-chart, plug in values for x, solve for y, plot those points:

y = (x+3)^2 - 14

x | y

------

0 | -5

etc.

The vertex form, though, says to draw a nice, boring parabola that has had its "normal" vertex of (0, 0) shifted. The equation:

y = (x+3)^2 - 14

has been shifted 3 spaces to the *left* and 14 spaces down...so the new vertex is at (-3, 14). Plug in other values for x and plot them, until you get it to cross the x-axis.

Hope that helps!