Convert to vertex form by completing the square. y = 4x^2 – 24x – 15
To convert the given quadratic equation to the vertex form by completing the square, follow these steps:
1. Begin by separating the constant term (15) from the x terms:
y = 4x^2 - 24x - 15
y = 4(x^2 - 6x) - 15
2. Take half of the coefficient of x (-6) and square it:
(-6/2)^2 = (-3)^2 = 9
3. Add the result from step 2 to the equation, but don't forget to also subtract the same value multiplied by the coefficient of x (4):
y = 4(x^2 - 6x + 9 - 9) - 15
4. Simplify the equation within the parentheses:
y = 4((x - 3)^2 - 9) - 15
5. Simplify further by expanding:
y = 4(x - 3)^2 - 36 - 15
6. Combine like terms:
y = 4(x - 3)^2 - 51
Therefore, the quadratic equation in vertex form is y = 4(x - 3)^2 - 51.