SOLUTION: [ Explain how to determine, without graphing, that the parabolic graph of a quadratic function will not have any x-intercepts. What is a real life example that can be represented b

Question 815387: [ Explain how to determine, without graphing, that the parabolic graph of a quadratic function will not have any x-intercepts. What is a real life example that can be represented by the quadratic function and the parabolic graph? What does the vertex represent in these cases? ]
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
for a general quadratic function in standard form:
y = ax^2 + bx + c
the parabolic graph may or may not have x-intercepts, depending on the value of the discriminant of the quadratic formula.
---
the discriminant and its rules are explained in the discriminant help text, here:
https://sooeet.com/math/quadratic-equation-solver.php
---
a real-life example:
h(t) = (�g/2)t^2 + Vt + H
---
the above is the equation of projectile motion, were g is acceleration due to gravity, V is the initial vertical velocity of the object, H is the initial height of the object, and t is time
---
in the above equation of projectile motion the vertex of the parabola represents the maximum height achieved by the projectile.
---
Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
---
Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
---
Convert fractions, decimals, and percents:
https://sooeet.com/math/fraction-decimal-percent.php
---
Calculate and graph the linear regression of any data set:
https://sooeet.com/math/linear-regression.php
RELATED QUESTIONS
Given the rational function f(x)=2x/x+4 I need to find the domain,find the equation of... (answered by edjones)

last question. I have a problem figuring out how to graph the quadratic function. I... (answered by rapaljer)

How are the zeros for a function (the values that make the function value equal zero),... (answered by Earlsdon)

I have to determine whether the equation represents a quadratic relationship without... (answered by MathLover1)

Without graphing, find the vertex. f(x) = (x + 3)2 + 3 Without graphing, find the... (answered by htmentor)

I hope someone can help me with this problem. I have the function f(x)=sqrt(x^2+81)-15. (answered by solver91311)

Explain how to tell from a quadratic equation what type of conic section the equation... (answered by stanbon)

Determine, without graphing, whether the given quadratic function has a maximum value or... (answered by ikleyn,solver91311)