x coordinate of vertex
y coordinate of vertex
Vertex
Answer:
(1, -16)
Step-by-step explanation:
Vertex form of a quadratic equation:
[tex]y=a(x-h)^2+k[/tex]
where:
Given equation:
[tex]x^2-2x-15=y[/tex]
To convert the given quadratic equation to vertex form, complete the square.
Add 15 to both sides:
[tex]\implies x^2-2x-15+15=y+15[/tex]
[tex]\implies x^2-2x=y+15[/tex]
Add the square of half the coefficient of the [tex]x[/tex] term to both sides:
[tex]\implies x^2-2x+\left(\dfrac{-2}{2}\right)^2=y+15+\left(\dfrac{-2}{2}\right)^2[/tex]
[tex]\implies x^2-2x+1=y+16[/tex]
Factor the left side:
[tex]\implies (x-1)^2=y+16[/tex]
Subtract 16 from both sides:
[tex]\implies (x-1)^2-16=y[/tex]
[tex]\implies y=(x-1)^2-16[/tex]
Comparing with the vertex form:
[tex]\implies h=1, \quad k=-16[/tex]
Therefore, the vertex of the given quadratic is (1, -16)
