2.03 Graph quadratics
Worked Examples
Question 1
Use your calculator or other handheld technology to graph $y=3x^2+18x+36$y=3x2+18x+36.
Then answer the following questions.
Is the graph concave up or concave down?
Concave up
AConcave down
BWhat is the minimum $y$y-value?
What is the $x$x-value corresponding to the minimum $y$y-value?
For what values of $x$x is the parabola decreasing?
Give your answer as an inequality.
Question 2
Use your calculator or other handheld technology to graph $y=4x^2-64x+263$y=4x2−64x+263.
Then answer the following questions.
What is the vertex of the graph?
Give your answer in coordinate form.
The vertex is $\left(\editable{},\editable{}\right)$(,)
What is the $y$y-intercept?
Give your answer in coordinate form.
The $y$y-intercept is $\left(\editable{},\editable{}\right)$(,)
Question 3
An object launched from the ground has a height (in metres) after $t$t seconds that is modelled by the equation $y=-4.9t^2+58.8t$y=−4.9t2+58.8t.
Graph this equation using a calculator or other technology then answer the following questions.
What is the maximum height of the object?
After how many seconds is the object at its maximum height?
After how many seconds does the object return to the ground?