Exercises: Graph Linear and Quadratic Functions and Show Intercepts, Maxima, and Minima

What is the slope of the line $f(x) = -3x + 7$?

What is the $y$-intercept of the line $3x + 4y = 12$?

For a quadratic function $f(x) = ax^2 + bx + c$, which condition tells you the graph opens downward and the vertex is a maximum?

What is the $x$-intercept of the line $f(x) = 4x - 8$?

The line $y - 5 = 3(x - 2)$ is in point-slope form. Which of the following correctly identifies the slope and a point on the line?

For $f(x) = x^2 - 6x + 5$, find the following without graphing:
(a) the $y$-intercept,
(b) the axis of symmetry,
(c) the vertex,
(d) the $x$-intercepts (if any).
State whether the vertex is a maximum or minimum.

For $g(x) = -2x^2 + 8x - 3$, find:
(a) the axis of symmetry,
(b) the vertex,
(c) the $y$-intercept.
Does the graph have a maximum or minimum? What is that value?

For $h(x) = x^2 + 2x + 5$, compute the discriminant. How many $x$-intercepts does the graph have? Find the vertex and $y$-intercept, and describe the graph.