Graphing
What is the first step in graphing a quadratic function from an equation?
Identify the sign of the leading coefficient a (to determine if it opens up or down) OR Find the axis of symmetry
What is the slope of the line y = 2x − 5?
2
What is the vertex of the parabola f(x) = (x − 3)² + 2?
(3, 2)
What does the leading coefficient tell you about a parabola?
Whether it opens upward (positive a) or downward (negative a), and how wide or narrow it is
What is the standard form of a quadratic equation?
f(x) = ax² + bx + c or ax² + bx + c = 0
What show do you recommend Mr. Laverde watch?
I need a new show!!!
Write the equation of a line with slope 3 and y-intercept −2 in slope-intercept form.
y = 3x − 2
What is the equation of the axis of symmetry for f(x) = x² − 4x + 3?
x = 2
Does the parabola f(x) = −3x² + 2x − 1 open upward or downward?
Downward
Solve the quadratic equation x² − 5x + 6 = 0 by factoring.
x = 2 or x = 3
How many x-intercepts can a parabola have? List all possibilities.
0, 1, or 2 x-intercepts
What movie do you recommend Mr. Laverde watch?
It better be good or I will fail you!!!!
If the vertex of a parabola is at (−1, 5), is the vertex a minimum or maximum if the parabola opens upward?
Minimum
When is Laverde's birthday?
March 19th aka TOMORROW!!!!!!!
What is the quadratic formula?
Write quadratic formula on board for students
What are the coordinates of the y-intercept of the parabola f(x) = 3x² − 2x + 5?
(0, 5)
Find the slope of the line passing through the points (2, 3) and (5, 9).
2
Find the vertex of the parabola f(x) = 2x² + 8x + 1 using the axis of symmetry formula.
(−2, −7)
If a parabola has a leading coefficient of −2, what can you conclude about its shape and direction?
It opens downward (negative) and is narrower than y = x² because the absolute value 2 is larger than 1
Use the quadratic formula to solve 2x² − 3x − 2 = 0.
x = 2 or x = −1/2
Explain why the axis of symmetry passes through the vertex of a parabola and how to find it from a quadratic equation in standard form.
The parabola is symmetric about the axis of symmetry, so the vertex (the highest or lowest point) must lie on this line. Find it using x = −b/(2a), where a and b are coefficients from f(x) = ax² + bx + c
Write the equation of the line passing through (1, 2) and (3, 6) in slope-intercept form.
y = 2x
Explain the difference between "vertex" and "axis of symmetry" and why every parabola has exactly one of each.
The vertex is the highest or lowest point (a point with coordinates). The axis of symmetry is a vertical line that passes through the vertex. Every parabola has exactly one vertex and exactly one axis of symmetry because it's a smooth, continuous curve with a single turning point.
What is Mr. Laverde's zodiac sign?
Pisces or Pisces Aries cusp
What is a song you recommend Laverde listen to?
it better be good or minus 100