Quadratic Function Real Life Examples and Applications

Use the following quadratic function to answer the question below: ${\displaystyle y=x^2-14x+5}$
a. Showing all work, find the vertwx of the quadratic.
b. Write the quadratic in the vertex form

Evaluate the limit.
${\displaystyle \underset{x\to 3}{lim}\frac{x^3-27}{x^2-9}}$

You have been asked to bake the birthday cake of a little girl who is about to turn three. When looking up suggestions online on how to bake this cake, you found that most everyone suggests baking the cake in smaller circular cake pans that have a diameter of 6 inches. That’s the best way to get the height for the unicorn head. A normal circular cake pan (and the only kind you have) has a diameter of 9 inches. You need to buy cake pans. As an experienced baker, you know that the recipe you are planning on using usually fills two regular (9-inch) cake pans, with a little room to spare. How many 6-inch pans do you need to buy? (We’re going to assume that all cake pans are the same height.)

Explain how to complete the square for an expression of the form $x^2+bx.$
Add ? to ${\displaystyle x^2+bx.}$

Solve ${\displaystyle 2\cos 2x-3\sin x=0f\text{or}{0}^{\circ }\le x\le {360}^{\circ }.}$

Quadratic equation solve $x2+2x-8=0$

${\displaystyle \left(\frac{\sqrt{12w^5}}{3w}\right)}$

Is 3m+8=15 is quadratic?

What is a quadratic equation in standard form with rational coefficients that has a root of 5 + 4i?

${\displaystyle x²-5x=18+2x}$

Consider the polynomial ${\displaystyle f\left(X\right)=x^4+1}$
a) Explain why f has no real roots, and why this means f mustfactor as a product of two ireducible quadratics.
b) Factor f and find all of its complex roots.

${\displaystyle x^2+2x-1=x^2-x+2}$

What is the complete factorization of ${\displaystyle 6x^4+12x^2}$?

${\displaystyle y=x^2-4x+3}$

Solve the quadratic: ${\displaystyle -4x^2–15x+4=0}$

Quadratics by factoring ${\displaystyle 2z(5z-2)=-5z+2}$

Factor $8z^3+1$ completely. Answer:

The square root of a number is between 7 and 8. Which could be the number? *

Which of the following is/are always false ?
(a) A quadratic equation with rational coefficients has zero or two irrational roots.
(b) A quadratic equation with real coefficients has zero or two non - real roots
(c) A quadratic equation with irrational coefficients has zero or two rational roots.
(d) A quadratic equation with integer coefficients has zero or two irrational roots.