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PilotLPTM [1.2K]
3 years ago
6

If a quadratic polynomial has an absolute minimum at (-3,-5), what is the range of the polynomial?

Mathematics
1 answer:
irga5000 [103]3 years ago
3 0

Answer:

range: (-5, ∞)

domain: (-∞, ∞)

Step-by-step explanation:

given vertex, absolute minimum: (-3, -5)

Range look at y-value

(minimum, maximum) the -5 will be on the left  of the comma b/c its the min

If this was a max, you would put the y-value on the right side of the comma

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3 years ago
How do I find if this type of equation has one solution two solutions or no solution 5x^2+14=19 I tried using the b^-4ac method
mash [69]

Answer:

x = 5 and x = -19

Step-by-step explanation:

You're on the right track.  It's the "discriminant" that tells you what you want to know here.  Before starting, arrange the terms of your quadratic in descending orders of x:  5x^2 + 14x - 19 = 0 (Note that I assumed you meant 14x instead of just 14).

Then the coefficients of this quadratic are a = 5, b = 14 and c = -19.

You are referring to the "quadratic formula."  It states this:

      -b ± √(b²-4ac)

x = -----------------------

               2a                                        

So, we insert the a, b and c values as indicated above:

      -14 ± √( 14² - 4[5][-19] )        -14 ± √(196 - 4[5][-19] )        -14 ± √576

x = ----------------------------------- = ---------------------------------- = ----------------------

                 2(10)                                 20                                      20

This comes out to:

x = (-14 + 24) / 2      and     x = (-14 - 24) / 2

or:

x = 5 and x = -19

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You replace x with 3 and y with -2 so
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