1. quadratic function/inequality, multi-step problem and I am stuck

Hi everyone, happy Tuesday!

I am taking algebra and I just don't get quadratics. I have a sheet of different quadratic questions I have been working on since yesterday, trying to figure it out before coming here, but I failed

I have a couple questions below, thank you in advance for your help

2. f(x)=2+5x-3x^2
a. determine if it goes up or down..... down I got that far
b. find the vertex, this is where I got stuck
c. find axis of symmetry
d. find x- and y- intercepts
e. sketch the graph y=f(x)
f. determine whether the function has a maximum value or a minimum value, then find this value (What, I am so lost!)
g. find the range of f.

ahh why are there so many questions for one function!

3.) I am stuck on this one because the fractions killed me, er

1/2x^2 - 3/4x + 7 <(or equal, didn't know how to add the bar under) 0

2. Originally Posted by GatorGirl
2. f(x)=2+5x-3x^2
a. determine if it goes up or down..... down I got that far
I don't know what this means...? Since the quadratic is negative, the parabola does open downward....

Originally Posted by GatorGirl
b. find the vertex, this is where I got stuck
To find the vertex, either complete the square or else use the formula "h = -b/(2a)".

Originally Posted by GatorGirl
c. find axis of symmetry
The axis of symmetry is the vertical line "x = h" through the vertex.

Originally Posted by GatorGirl
d. find x- and y- intercepts
To find a given intercept, plug "0" in for the other variable, and solve. So plug "0" in for "x" and evaluate to find the y-intercept, and then plug "0" in for "y" and solve the quadratic equation to find the x-intercept(s).

Originally Posted by GatorGirl
e. sketch the graph y=f(x)
Graph in the usual way: Pick x-values, plug them into the formula, find the corresponding y-values, and draw the dots. Repeat until you are confident of the shape of the curve, and then sketch.

Originally Posted by GatorGirl
f. determine whether the function has a maximum value or a minimum value, then find this value (What, I am so lost!)
Look at the graph. Look at the vertex. Use what you've learned about the relationship between the vertex of a parabola and the max/min points of quadratics.

Originally Posted by GatorGirl
g. find the range of f.
The range is the output values. So look at the graph and figure out what values y can achieve. For instance, can y equal 5?

Originally Posted by GatorGirl

1/2x^2 - 3/4x + 7 <(or equal, didn't know how to add the bar under) 0
To learn how to answer this, study a lesson on solving quadratic inequalities.

3. well. This looks like a perfect opportunity to try out latix , excuse me if i make a mistake.

I will help you with number 2, how to find the axis of symmetry.

So.. The Equation is ( i think, someone correct me if i am wrong):

$-3x^2\oplus5x\oplus2$

The formula to find the axis of symmetry is $\frac{-b}{2a}$

The standard form of a quadratic equation is: ax^2+bx+c (by the way guys, when i tried to do this in LATEX, it said error...)

So, just look at your equation, and find the $-b$(b is 5, so -b is -5) then find the $a$ (the a is -3, -3 times 2 is -6) and plug them into the equation, and that will give you the axis of symmetry.

So, the axis of symmetry is: $\frac{-5}{-6}$ which simplifies to $\frac{5}{6}$