write in vertex form (by completing the square)y=4x2+40x+96
To write the quadratic equation y = 4x^2 + 40x + 96 in vertex form by completing the square, follow these steps:
Step 1: Inspect the coefficient in front of the x^2 term to identify the value of "a". In this case, a = 4.
Step 2: Divide the coefficient of the x term by 2, square the result, and add it to both sides of the equation. This completes the square for the x terms.
Let's calculate this:
x-coordinate of the vertex = -b/2a
x-coordinate of the vertex = -40 / (2 * 4) = -40 / 8 = -5
Now let's substitute the x-coordinate of the vertex back into the equation to find the y-coordinate of the vertex.
y = 4 * (-5)^2 + 40 * (-5) + 96
y = 4 * 25 - 200 + 96
y = 100 - 200 + 96
y = -4
Therefore, the vertex is (-5, -4).
Step 3: Rewrite the equation using the vertex form, which is y = a(x - h)^2 + k, where (h, k) represents the vertex coordinates.
Using the vertex coordinates obtained, the equation becomes:
y = 4(x + 5)^2 - 4
So, the quadratic equation y = 4x^2 + 40x + 96 can be rewritten in vertex form as y = 4(x + 5)^2 - 4.