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,
To determine if your answer is correct, we need to convert the quadratic function y = 4(x+5)(x-2) into the vertex form.
To write the quadratic function in vertex form, we need to complete the square.
First, let's expand the equation:
y = 4(x² + 3x - 10)
Next, we need to find the value that completes the square for the quadratic term. In this case, the coefficient of the x term is 3, so we need to add (3/2)² = 9/4 to both sides of the equation:
y + 4(9/4) = 4(x² + 3x - 10 + 9/4)
Now, we can simplify the right side of the equation by factoring the quadratic expression:
y + 9 = 4(x² + 3x - 1/4)
To complete the square, we need to add (3/2)² = 9/4 inside the parentheses:
y + 9 = 4(x² + 3x + 9/4 - 9/4 - 1/4)
Simplifying further:
y + 9 = 4(x² + 3x + 8/4)
y + 9 = 4(x² + 3x + 2)
Now, factor the perfect square trinomial:
y + 9 = 4(x + (3/2))²
Finally, rearrange the equation to isolate y:
y = 4(x + (3/2))² - 9
So, the correct answer in vertex form is:
y = 4(x + (3/2))² - 9
Comparing this with your answer, y = 4(x+3/2)² - 49, we can see that your final constant term is not calculated correctly. It should be -9, not -49.
Therefore, your answer for the vertex form is not correct.