Question Video: Finding the Value of the Constant In a Quadratic Function Given Its Vertex Coordinates Mathematics • Second Year of Secondary School

Video Transcript

The figure below represents the function 𝑦 is equal to 𝑥 squared plus 𝑚. Find the value of 𝑚 given that the length 𝑂𝐴 is four units.

In this question, we are told that the equation of the function is 𝑦 is equal to 𝑥 squared plus 𝑚. We are asked to find the value of 𝑚 given that the length 𝑂𝐴 is four units. Since our leading term is 𝑥 squared, we know that our function is a quadratic. We also know that the function 𝑦 equals 𝑥 squared passes through the origin as shown. Our function is a translation of this, four units in the negative 𝑦-direction. The graph has moved four units down. This means that it has equation 𝑦 is equal to 𝑥 squared minus four.

The value of 𝑚 given that the length 𝑂𝐴 is four units is negative four. This is because the minimum point of our function has coordinates zero, negative four.