Write the number and the nature of the roots of the quadratic

Mathematics

1 answer:

schepotkina [342]3 years ago

3 0

Answer:

two unequal real roots

Step-by-step explanation:

35 - 5(4)(-3) simplifies to 35 + 60, or 95.

Because the discriminant is positive, the quadratic has two unequal real roots.

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$\bf \stackrel{\textit{vertex}}{(3,-2)}~~ \begin{cases} h = 3\\ k = -2 \end{cases}\implies y=a(x-3)^2-2 \\\\\\ \stackrel{\textit{passes through}}{(5,-1)}~~ \begin{cases} x=5\\ y= -1 \end{cases}\implies -1=a(5-3)^2-2\implies 1=a(2)^2 \\\\\\ 1=4a\implies \cfrac{1}{4}=a~\hfill \boxed{y=\cfrac{1}{4}(x-3)^2-2}$

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3 years ago

Read 2 more answers

The sum of two numbers is 14. The first number is 2/5 of the second number. What are the numbers?

zlopas [31]

Answer:

4 and 10

Step-by-step explanation:

To solve this problem, we need to find all the numbers between 1 and 13 that have a sum of 14. The list is shown below:

1 + 13, 2 + 12, 3 + 11, 4 + 10, 5 + 9, 6 + 8, 7 + 7

Now we must figure out which set of numbers include one number that is 2/5 of the value of the other. We can do that by turning the sets of numbers into fractions as shown below:

$\frac{1}{13}\neq \frac{2}{5}$