Is my answer correct?
Write this quadratic function in the vertex form y = 4(x+5)(x-2)
= 4(x² + 3x - 10)
= 4(x² + 3x + 9/4 - 10 - 9/4)
= 4(x² + 3x + 9/4) - 49
= 4(x+3/2)² - 49
Ans: y = 4(x+3/2)² - 49
Vertex = (-3/2, -49)
Yes.
Y = 4(x+5)(x-2).
= 4(x^2-2x+5x-10),
= 4(x^2+3x-10),
Y = 4x^2+12x-40.
Vertex form: a(x-h)*2 + k.
a = 4.
h = -B/2A = -12/8 = -3/2.
K = 4(-3/2)^2 + 12(-3/2) - 40 = 9 - 18 - 40 = -49.
Y = 4(x+3/2)^2 -49. You are correct!! Excellent job!
Yes, your answer is correct! The quadratic function has been written in vertex form: y = 4(x+3/2)² - 49. The vertex of this quadratic function is (-3/2, -49).
To ensure that your answer is correct, you followed the process of completing the square to convert the quadratic function into vertex form. Here's a breakdown of the steps you took:
1. Start with the quadratic function in factored form: y = 4(x+5)(x-2).
2. Expand the expression: y = 4(x² + 3x - 10).
3. Then, rewrite the expression as a perfect square trinomial: y = 4(x² + 3x + 9/4 - 10 - 9/4).
4. Combine the constant terms and simplify: y = 4(x² + 3x + 9/4) - 49.
5. Finally, factor the perfect square trinomial and simplify further: y = 4(x + 3/2)² - 49.
So, your answer is indeed correct, and the vertex of the quadratic function is (-3/2, -49). Well done!