Exam 3: Quadratic Functions

Is the graph of $y=4(6-4 x)(x-4)$ concave up or concave down?

For $f(x)=x^{2}$ , does $f\left(\frac{4}{7}\right)=\frac{f(4)}{f(7)}$ ?

Which of the following quadratic functions have zeros at $x=-4$ and $x=1$ ?

A relief package is dropped from an airplane and falls to the ground along a parabolic path, starting at the vertex of the parabola. The package was released when the plane was directly above a marker at a height of 5 kilometers, and the package hits the ground 4.63 kilometers from the marker. If $h$ is the height of the package when it is a horizontal distance $d$ from the marker, the equation for $h$ in terms of $d$ is given by $h(d)=a d^{2}+b d+c$ , where $a=\ldots, b=\ldots$ , and $c=\ldots$ . Round any decimals to 3 places.

Find the zeros of $Q(r)=2 r-15+r^{2}$ by factoring. List the answers in the form "A, $\mathrm{B}$ ", with $\mathrm{A}<\mathrm{B}$ .

Suppose a farmer has 160 feet of fence and he wants to enclose a pasture with a rectangular boundary. There is already fencing along one side of the field that he wants to enclose, so he will only need to fence 3 sides of the new field. What are the dimension of the field that will give maximum area.

The graph of $r(t)=4 t^{2}-40 t+104$ has vertex (---------,--------- ) and axis of symmetry $x=$ --------

A projectile's height $h(t)$ above ground in feet is a quadratic function of time $t$ in seconds since launched. Three values of the function are given in the table below. What is the maximum number of feet above the ground that the projectile reaches?

A projectile's height $h(t)$ above ground is a quadratic function of time $t$ in seconds since launched. Three values of the function are given in the table below. How many seconds does it take for the projectile to hit the ground?

Solve $3.2 x^{2}-4.5 x=6.5$ by the quadratic formula. Round your answers to 2 decimal places. List the answers in the form "A, B", with $\mathrm{A}<\mathrm{B}$ .

The following figure gives the graph of $y=f(x)$ , a quadratic function with vertex (3, 2). The formula for $f(x)$ is $y=a(x-b)^{2}+c$ , where $a=$ ---------- $b=$ ----------- , and $c=$ ------------

The vertex form of $f(x)=x^{2}+4 x-1$ is $f(x)=(x+a)^{2}-b$ , where $a=$ ----------- and $b=$ ------------

Suppose $g(x)=4 x^{2}-7 x$ . What is $g(x+h)$ ?

The height of an object above the ground is described by the function $f(t)=2.3 t^{2}-14 t+4$ . a) What is the initial height of the object at time $t=0$ ? b) When does the object have height 2 ?

Which of the following quadratic functions have zeros at $x=6$ and $x=-6$

Select the quadratic functions that are concave upward.

Convert the quadratic function $y=x^{2}+10 x+28$ to vertex form. Identify the vertex and the axis of symmetry.

Find a formula in terms of $f(x)=x^{2}$ for $g(x)=x^{2}+6 x+2$ .

How many distinct real roots does the function $y=x^{2}-4 x+7$ have?

The formula for the following parabola is $f(x)=a(x-h)^{2}+k$ , where $a=$ -------- $h=$ --------- , and $k=$ -------- Note: Figure is not necessarily drawn to scale.