6.1 - 6.4 Flashcards
(13 cards)
How can you tell if two parabolas are congruent?
If their coefficients of x², or “a”, are equal in magnitude, regardless of sign.
What does it mean if two parabolas are congruent?
They have the same shape
How do you find the vertex from standard from?
- Find the x-coordinate of the vertex, or “p”, by finding the average of the 2 x-intercepts. (add together and divide by two)
- Find the y-coordinate of the vertex, or “q”, by substituting the x-coord. into the equation and solving for y.
- State the vertex in a ‘therefore’ statement.
How do you sketch a parabola from standard form?
- Calculate the discriminant to check for number of roots (b² - 4ac)
- Let y=0, then solve the equation by factoring (2 numbers that add to “b”, multiply to “c”). These roots are the x-intercepts.
- Find “p” by averaging the x-ints
- Find “q” by substituting “p” into the original equation
- State the vertex
- Plot the intercepts and the vertex, the draw a smooth curve. Label the parabola with its equation.
What does “a” in vertex form tell us about the parabola of the equation?
“a” tells us direction and shape
- positive opens up, negative opens down
- > 1 = vertical stretch; long and narrow parabola
- 0<a></a>
What do “p” and “q” in vertex from tell us about the parabola of the equation?
“p” and “q” are the coordinates of the vertex
- the sign of “p” is opposite to the one it has in the equation because of the formula’s negative sign
- if it seems one them isn’t written, it means that one is equal to 0
- “p” causes horizontal shift/translation left and right
- “q” causes vertical shift/translation up and down
What is the axis of symmetry’s equation?
x = p
This is where “p” is the x-coordinate of the vertex
How do you sketch a parabola from vertex form?
- plot the vertex, your starting point
- identify the “a” value (sign and number)
- determine the step pattern (1a, 3a, 5a)
How do you put a standard from equation into vertex form?
Complete the square
How do you complete the square to put a standard from equation into vertex form?
- divide out the a-value from the 1st two terms
- find the magic number using the coefficient of x. Then within the brackets, add and subtract the magic number in that order
- write the 1st three terms as a binomial square (sq. root, sign, sq. root)
- multiply the 4th term in the brackets by “a” to take it out of the brackets
- now it can be graphed
When does a parabola have a minimum value?
If “a” is positive; if the parabola opens up.
When does a parabola have a maximum value?
If “a” is negative; if the parabola opens down
How do you find and write the maximum or minimum value of a parabola?
“This parabola has a min/max value of “q” when x = “p”.
