What's the vertex form of [tex]y = x^2 - 20x + 15[/tex]?

this looks like a parabola so: y=x^2 - 20x + 15 --> x^2 - 20x +15=y (x^2 -20x)=y - 15 --> (x - 10)^2=y - 15 +100 ( used complete the square) (x - 10)^2=y + 85

Answered by bglotr | 2024-06-10

To convert the quadratic equation y = x 2 - 20x + 15 to vertex form, complete the square for the x terms, resulting in y = ( x − 10 ) 2 - 85, which shows that the vertex of the parabola is at the point (10, -85).
The question asks for the vertex form of the quadratic equation y = x 2 - 20x + 15. The vertex form of a quadratic equation is given by y = a ( x − h ) 2 + k, where (h, k) is the vertex of the parabola. To convert the given quadratic equation into vertex form, we will complete the square.
First, we factor out the coefficient of the x 2 term, but in this case, it is 1, so we don't need to factor anything. Then, we rearrange the equation and complete the square on the x terms:

y = x 2 - 20x + 15
y = ( x 2 - 20x + 100) - 100 + 15
y = ( x − 10 ) 2 - 85

The completed equation, (x - 10)^2 - 85, is now in vertex form, where the vertex of the parabola is at (10, -85).

Answered by BurtLancaster | 2024-06-25

The vertex form of the equation y = x 2 − 20 x + 15 is y = ( x − 10 ) 2 − 85 . This was derived by completing the square on the original quadratic equation. The vertex of this parabola is at the point ( 10 , − 85 ) .
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Answered by bglotr | 2024-12-23