State the zeros, vertex, and equation of the axis of symmetry of the parabola at the right.
The points (-9, 0)
and (19, 0)
lie on a parabola.
a) Determine an equation for its axis of symmetry.
b) The y—coordinate of the vertex is -28. Determine an equation for the parabola in factored form.
c) Write your equation for part b) in standard form.
Decide, without graphing, whether each data set can be modelled by a quadratic relation. Explain how you made your decision.
Decide, without graphing, whether each data set can be modelled by a quadratic relation. Explain how you made your decision.
Sketch each graph. Label the intercepts and the vertex using their coordinates.
\displaystyle
y = (x-6)(x + 2)
Sketch each graph. Label the intercepts and the vertex using their coordinates.
\displaystyle
y = -(x-6)(x + 4)
The population, P
, of a city is modelled by the equation P = 14t^2 + 820t + 42 000
, where tis the time in years.
When t = 0
, the year is 2008.
a) Determine the population in 2018.
b) When was population about 30 000?
Expand and simplify.
\displaystyle
(3x -3)(5x + 2)
Expand and simplify.
\displaystyle
(3x -4y)(5x + 2y)
Expand and simplify.
\displaystyle
-5(x -4)^2
A toy rocket is placed on a tower and launched straight up. The table shows its height, y
, in metres above the ground after x
seconds.
a) What is the height of the tower?
b) How long is the rocket in flight?
c) Do the data in the table represent a quadratic relation? Explain.
d) Create a scatter plot. Then draw a curve of good fit.
e) Determine the equation of your curve of good fit.
f) What is the maximum height of the rocket?
Evaluate.
a) \displaystyle
7^{-2}
b) \displaystyle
-3^0
Evaluate.
a) \displaystyle
-(\frac{2}{3})^{-4}
b) \displaystyle
-5^{-3}