Applications of Quadratic Functions

Key Questions

How can quadratic equations be used to model ballistics?

The height $H$ $H$ of a projectile above the ground after $t$ $t$ seconds is given by the formula $H_{t} = - \frac{1}{2} \cdot g \cdot t^{2} + V_{0} \cdot t + H_{0}$ $H_t = -1/2*g*t^2 + V_0*t + H_0$ ,
where $g$ $g$ is a physical constant (gravitational acceleration $\approx 9.8 \frac{m}{s^{2}}$ $~~9.8 m/s^2$ ), $V_{o}$ $V_o$ is the initial velocity and $H_{0}$ $H_0$ is the initial height.

We notice that this is a quadratic equation of variable $t$ $t$ .

Alex Boroda · 1 · May 27 2015

Questions

What are common mistakes students make with applications of quadratic functions?
How is gravity a quadratic function?
How can quadratic equations be used to model ballistics?
What is the largest area that can be enclosed by a rectangular fence with a total perimeter of 500 m?
In a word problem about ballistics, what do the x-intercepts of a quadratic function represent?
In a word problem about ballistics, what does the absolute maximum of a quadratic function represent?
How do I solve the formula $16 t^{2} - 12 t - h = 0$ $16t^2 - 12t - h = 0$ for $t$ $t$ ?
How do I solve the formula $16 t^{2} - v t - 40 = 0$ $16t^2 - vt - 40 = 0$ for $t$ $t$ ?
How do I solve the formula $k x^{2} + 8 x + 4 = 0$ $kx^2 + 8x + 4 = 0$ for $x$ $x$ ?
If the roots of $2 x^{2} + 4 x - 1 = 0$ $2x^2+4x-1=0$ are $a$ $a$ and $b$ $b$ , find $a^{2} + b^{2}$ $a^2+b^2$ ?
What is the square root of $3 - 2 \sqrt{2}$ $3-2sqrt2$ ?
How do you find two quadratic function one that opens up and one that opens downward whose graphs have intercepts (-1,0), (3,0)?
How do you find two quadratic function one that opens up and one that opens downward whose graphs have intercepts (-5,0), (5,0)?
How do you find two quadratic function one that opens up and one that opens downward whose graphs have intercepts (0,0), (10,0)?
How do you find two quadratic function one that opens up and one that opens downward whose graphs have intercepts (4,0), (8,0)?
How do you find two quadratic function one that opens up and one that opens downward whose graphs have intercepts (-3,0), (-1/2,0)?
How do you find two quadratic function one that opens up and one that opens downward whose graphs have intercepts (-5/2,0), (2,0)?
Question #5059c
How can we attempt to simplify expressions of the form $\sqrt{p + q \sqrt{r}}$ $sqrt(p+qsqrt(r))$ where $p, q, r$ $p, q, r$ are rational?
It is known that the equation $b x^{2} - (a - 3 b) x + b = 0$ $bx^2-(a-3b)x+b=0$ has one real root. Prove that the equation $x^{2} + (a - b) x + (a b - b^{2} + 1) = 0$ $x^2+(a-b)x+(ab-b^2+1)=0$ has no real roots.?

Linear and Quadratic Functions

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Linear Functions and Graphs
Average Rate of Change
Linear Correlation and Modeling
Graphing Quadratic Functions
Applications of Quadratic Functions
Linear and Quadratic Functions on a Graphing Calculator
Completing the Square
The Quadratic Formula

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Applications of Quadratic Functions

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Linear and Quadratic Functions