Is the vertex the maximum or the minimum of this quadratic

Question

Assignment

Question 1. Which of the following functions are linear or quadratic? If a function is linear, what is its slope and its y-intercept? Is it increasing or decreasing? If a function is quadratic, is it concave up or concave down?

(a) y = (x - 5)² - 7,

(b) y = (x + 3)³ - 1,

(c) y = 3x - 19,

(d) y = -8 + (3x² - 1)(1 + x),

(e) y = -x² + 4x - 2/3,

(f) y = 5/2 x + x²,

(g) y - 7 - x² = x,

(h) y = 99.

Question 2. Sketch the graph of the function y = 3x - 6. Write the formula for the inverse of this function and sketch the graph of the inverse in the same coordinate system.

Question 3. A straight line passes through the points (-1, 5) and (1, -2). Find the equation of the straight line.

Question 4.

(a) Sketch the graph of the function y = x².

(b) Sketch the graph of the function y = (x + 1)².

(c) Sketch the graph of the function y = (x + 1)² - 3.

(d) Give the coordinates of the vertex of the parabola from part (c).

(e) Convert the vertex form from part (c) into the general form of a quadratic function.

Question 5. Is the function y = 9x², defined on the domain R with the codomain [0, ∞), invertible? Will it be invertible if we restrict the domain to the interval [0, ∞)? If not, explain why. If yes, write the formula for the inverse function.

Question 6. Solve the equation x² - 5x + 6 = 0.

Question 7. Find the vertex of the parabola

y = -x² + 5x - 6.

Is the vertex the maximum or the minimum of this quadratic function?