Please provide solutions so I can explain it better to my child. Thank you

1. Connecting to a Calculus Concept: Concavity The function f(z) = z2 is concave up. One way to define this property for the function f(z) ==? is: If P = (a,0?) and Q = (b,?) are two unique points on the graph of f(z) = z? then the line segment PQ (except the endpoints at a and b) always lies above the graph of f(z) == (a) Sketch a graph that illustrates the statement above. (b) Find the slope of the line that passes through any points P and Q. Notice anything interesting about the simplified value for the slope? Explain. Verify it with an example. (c) Find the equation of the secant line that passes through any points P and Q and algebraically verify that the midpoint of segment PQ lies above the parabola. (d) Explain verbally how the conclusion from your algebraic verification in (c) proves that the midpoint of segment PQ lies above the parabola. . 1. Practice with Factoring (a) Find or create a problem that requires factoring by grouping and solve. (b) Find and record the rule for factoring the difference of two squares, the sum of two cubes and the difference of two cubes. (c) The sum of two squares can be factored, but this is generally not done (at least not in our course). Why might this be so? ; (d) Factor and simplify the expression 'Ll'-zgz"z_f;\"@. . . 2_1 2. Consider the equation y = Z=. (a) Factor and simplify the expression on the right. Confirm the result has the form y = z+1. (b) Graph bothy = "':_'11 and y = z+1 (two separate graphs). Be sure to note the difference in these two graphs. [HINT: The difference here is subtle and it's unlikely to show when __using a graphing utility like Desmos.] 3. Simplify the expression =5= by rationalizing the denominator. Vz+/5