In
[link] , the quadratic was easily solved by factoring. However, there are many quadratics that cannot be factored. We can solve these quadratics by first rewriting them in standard form.
Given a quadratic function, find the
intercepts by rewriting in standard form .
Substitute
and
into
Substitute
into the general form of the quadratic function to find
Rewrite the quadratic in standard form using
and
Solve for when the output of the function will be zero to find the
intercepts.
Finding the
Intercepts of a parabola
Find the
intercepts of the quadratic function
We begin by solving for when the output will be zero.
Because the quadratic is not easily factorable in this case, we solve for the intercepts by first rewriting the quadratic in standard form.
We know that
Then we solve for
and
So now we can rewrite in standard form.
We can now solve for when the output will be zero.
Applying the vertex and
x -intercepts of a parabola
A ball is thrown upward from the top of a 40 foot high building at a speed of 80 feet per second. The ball’s height above ground can be modeled by the equation
When does the ball reach the maximum height?
What is the maximum height of the ball?
When does the ball hit the ground?
The ball reaches the maximum height at the vertex of the parabola.
The ball reaches a maximum height after 2.5 seconds.
To find the maximum height, find the
coordinate of the vertex of the parabola.
The ball reaches a maximum height of 140 feet.
To find when the ball hits the ground, we need to determine when the height is zero,
We use the quadratic formula.
Because the square root does not simplify nicely, we can use a calculator to approximate the values of the solutions.
The second answer is outside the reasonable domain of our model, so we conclude the ball will hit the ground after about 5.458 seconds. See
[link]
A rock is thrown upward from the top of a 112-foot high cliff overlooking the ocean at a speed of 96 feet per second. The rock’s height above ocean can be modeled by the equation
The lymphatic system plays several crucial roles in the human body, functioning as a key component of the immune system and contributing to the maintenance of fluid balance. Its main functions include:
1. Immune Response: The lymphatic system produces and transports lymphocytes, which are a type of
asegid
to transport fluids fats proteins and lymphocytes to the blood stream as lymph
Anatomy is the study of the structure of the body, while physiology is the study of the function of the body. Anatomy looks at the body's organs and systems, while physiology looks at how those organs and systems work together to keep the body functioning.
Enzymes are proteins that help speed up chemical reactions in our bodies. Enzymes are essential for digestion, liver function and much more. Too much or too little of a certain enzyme can cause health problems
Kamara
yes
Prince
how does the stomach protect itself from the damaging effects of HCl
the normal temperature is 37°c or 98.6 °Fahrenheit is important for maintaining the homeostasis in the body
the body regular this temperature through the process called thermoregulation which involves brain skin muscle and other organ working together to maintain stable internal temperature