SOLUTION: sketch the parabola {{{ y = x^2-7x+12 }}} using the algorithm. Label axis of symetry, vertex, and x and y intercepts

Question 153203: sketch the parabola using the algorithm. Label axis of symetry, vertex, and x and y intercepts
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Vertex:

In order to find the vertex, we first need to find the x-coordinate of the vertex.

To find the x-coordinate of the vertex, use this formula: .

Start with the given formula.

From , we can see that , , and .

Plug in and .

Negate to get .

Multiply 2 and to get .

So the x-coordinate of the vertex is . Note: this means that the axis of symmetry is also .

Now that we know the x-coordinate of the vertex, we can use it to find the y-coordinate of the vertex.

Start with the given equation.

Plug in .

Square to get .

Multiply and to get .

Multiply and to get .

Combine like terms.

So the y-coordinate of the vertex is .

So the vertex is

which in decimal form is (3.5, -0.25).

------------------------------------------

x-intercept(s):

Start with the given equation.

Plug in y=0

Start with the given equation

Factor the left side (note: if you need help with factoring, check out this solver)

Now set each factor equal to zero:
or

or Now solve for x in each case

So the answers are

or

which means that the x-intercepts are (4,0) and (3,0)

--------------------------------------

y-intercept:

Start with the given equation.

Plug in x=0

Simplify

So the y-intercept is (0,12)

So with all of this info, we get this sketch:

Graph of

note: the point (7,12) is a reflection of the point (0,12)
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