Answer:
I was unclear if you needed this solved in vertex or standard form, so I gave you both.
Vertex form: [tex](x - 4)^2 - 1[/tex]
Standard form: [tex]x^2 - 8x + 15[/tex]
Step-by-step explanation:
This is a quadratic equation. In order to solve this problem, you will need these equations:
Vertex form: [tex]a(x - h)^2 + k[/tex]
Standard form: [tex]ax^2 + bx + c[/tex]
Starting with vertex form:
The vertex is (4, -1). When putting this into your equation, substitute the "x" value for h, and substitute the "y" value for k.
[tex]a(x - 4)^2 - 1[/tex]
You can disregard the "a" for this particular problem because it is equal to 1.
Standard form:
Now that you have vertex form, you can expand it into standard form.
[tex](x-4)^2 - 1[/tex]
Use the FOIL method to multiply (x - 4)(x - 4).
This will equal [tex]x^2 - 8x + 16[/tex].
Keep in mind that you still have a -1 from your original equation to take into account. Once you subtract 1, this will leave you with:
[tex]x^2 - 8x + 15[/tex]
