Answer:
Step-by-step explanation:
Let's take statement C and D.
For C;
Vertex means a single point of intersection of a curve formed from a quadratic equation when we assume the curve to be of equal half.
We can know this point by drawing a graph and locating the points X and Y where the curve gives a maximum curve or minimum curve because at that point the curve is divided in half.
And a straight line drawn through that point to divide the curve in two is the axis of symmetry. See attachment for more clarification.
For D,
When you plot the graph of the quadratic equations ;
To do that theoretically.
You find the dy/dx of the expression and equate it to zero;
Let's take an example
y = 4x^2 + 3x -6
dy/dx= 8x + 3; if we equate it to 0
We have 8x + 3 = 0
8x = -3
x = -3/8
Then if we substitute this value of X in
y= 4x^2 + 3x -6; we would get the value of y;
Now if y = negative we know we have a minimum graph but if Y is positive we have a maximum graph.
However without checking the value of y to determine if the graph is a positive or negative graph;
We can take the second derivative of y
This is. dy/ dx[8x + 3]
8
Since d^2y/ dx^2 =8; which is > 0; we know the equation has a maximum point
But if d^2y/ dx^2; we evaluate to less than zero. We know the quadratic equation gives a minimum point.
