Question

Please help me find the vertex of the following quadratic equation and explain how to find the vertex.

Answer 1

The vertex of the quadratic equation at² + bt + c = 0 is found by using the formula -b/(2a) for the x-coordinate, and then substituting this value back into the equation to find the y-coordinate.

Step-by-step explanation:

To find the vertex of the quadratic equation in the form at² + bt + c = 0, we can use the formula for the x-coordinate of the vertex, which is -b/(2a). For your given equation with coefficients a = 4.90, b = 14.3, and c = -20.0, you can calculate the x-coordinate of the vertex as follows:

x = -b / (2a) = -14.3 / (2 × 4.90) = -14.3 / 9.8 ≈ -1.46

Once you have the x-coordinate of the vertex, the y-coordinate can be found by substituting this value back into the original equation. Therefore, the vertex of the quadratic equation is approximately (-1.46, f(-1.46)).

Answer 2

The Solution:

Given:

We are asked to find the vertex of the given equation.

The Vertex formula for a Quadratic Equation is:

From the given equation, we have:

`y=7(x^2-8x+16)+14`
`\begin{gathered} y=7x^2-56x+112+14 \\ \\ y=7x^2-56x+126 \end{gathered}`

In this case,

`\begin{gathered} a=7 \\ b=-56 \\ c=126 \end{gathered}`

So, the vertex is:

`(h,k)=((-b)/(2a),(-(b^2-4ac))/(4a))=((-(-56))/(2(7)),(-[(-56)^2-4(7)(126))/(4(7)))=(4,-14)`

Therefore, the correct answer is:

`(h,k)=(4,-14)`