Question

write 2x^2+12x+4 in the form a(x+b)^2+c,where a,b and c are numbers .What are the values of a,b and c?Hence,write down the coordinates of the turning point of the curve y=2x^2 + 12x + 4.

Answer 1

To write 2x^2+12x+4 in the form a(x+b)^2+c, we complete the square. The values of a, b, and c are found to be 2, 3, and -14 respectively. The turning point of the curve is at the coordinates (-3,-14).

Step-by-step explanation:

To write 2x^2+12x+4 in the form a(x+b)^2+c, we need to complete the square. First, we factor out the coefficient of x^2, which is 2. We get 2(x^2+6x)+4. To complete the square, we take half of the coefficient of x, square it, and add it to the expression inside the parentheses. In this case, half of 6 is 3, and 3^2 is 9. So, we add 9 inside the parentheses. We get 2(x^2+6x+9)+4-18. Simplifying further, we have 2(x+3)^2-14. Therefore, a = 2, b = 3, and c = -14.

The coordinates of the turning point of the curve y=2x^2+12x+4 are (-3,-14).

Answer 2

To write the quadratic expression 2x^2 + 12x + 4 in the form a(x+b)^2 + c, we need to complete the square. Let's go through the steps:

Step 1: Factor out the coefficient of x^2 (a) from the quadratic expression:

2(x^2 + 6x) + 4

Step 2: Take half of the coefficient of x (b) and square it. In this case, b = 6, so (6/2)^2 = 9.

2(x^2 + 6x + 9) + 4 - 18

Step 3: Rewrite the expression inside the parentheses as a perfect square trinomial. In this case, (x + 3)^2.

2(x + 3)^2 + 4 - 18

Step 4: Simplify the expression by combining like terms.

2(x + 3)^2 - 14

So, the quadratic expression 2x^2 + 12x + 4 can be written in the form a(x+b)^2 + c as 2(x + 3)^2 - 14.

Now, let's find the coordinates of the turning point of the curve y = 2x^2 + 12x + 4.

The turning point of a quadratic function in the form y = ax^2 + bx + c is given by the coordinates (-b/2a, f(-b/2a)), where f(x) is the quadratic function.

In this case, a = 2, b = 12, and c = 4. Plugging these values into the formula, we get:

x = -12/(2*2) = -12/4 = -3

To find the y-coordinate, we substitute x = -3 into the equation y = 2x^2 + 12x + 4:

y = 2(-3)^2 + 12(-3) + 4 = 2(9) - 36 + 4 = 18 - 36 + 4 = -14

Therefore, the turning point of the curve y = 2x^2 + 12x + 4 is (-3, -14).