All categories

2 years ago

The zeros of a quadratic function are 2 and 4 what is the vertex of the function

1 answer:

3 0

The x-coordinate of the vertex is precisely halfway between the given roots 2 and 4; thus, x = (2+4)/2, or x=3. The y-coordinate is the value of the function at this x=3.

We can actually determine the equation of this quadratic from the zeros:

f(x) = (x-2)(x-4), or f(x) = x^2 - 6x + 8. To find the y-coord. of the vertex,, subst. 3 for x in f(x) = x^2 - 6x + 8: f(3) = 3^2 - 6(3) + 8 = 9 - 18 + 8, or -1. Then we know that the vertex is at (3, -1).

You might be interested in

Find the midpoint of the line segment with endpoints at the given coordinates (-6,6) and (-3,-9)

JulsSmile [24]

The midpoint of the line segment with endpoints at the given coordinates (-6,6) and (-3,-9) is $\left(\frac{-9}{2}, \frac{-3}{2}\right)$

<u>Solution:</u>

Given, two points are (-6, 6) and (-3, -9)

We have to find the midpoint of the segment formed by the given points.

The midpoint of a segment formed by $\left(\mathrm{x}_{1}, \mathrm{y}_{1}\right) \text { and }\left(\mathrm{x}_{2}, \mathrm{y}_{2}\right)$ is given by:

$\text { Mid point } \mathrm{m}=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)$

$\text { Here in our problem, } x_{1}=-6, y_{1}=6, x_{2}=-3 \text { and } y_{2}=-9$

Plugging in the values in formula, we get,

$\begin{array}{l}{m=\left(\frac{-6+(-3)}{2}, \frac{6+(-9)}{2}\right)=\left(\frac{-6-3}{2}, \frac{6-9}{2}\right)} \\\\ {=\left(\frac{-9}{2}, \frac{-3}{2}\right)}\end{array}$

Hence, the midpoint of the segment is $\left(\frac{-9}{2}, \frac{-3}{2}\right)$

6 0

2 years ago

Which route must use all of the vertices of a vertex-edge graph? (Check all that apply.)

zlopas [31]

An Euler path, in a graph or multi graph, is a walk through the graph which uses every edge exactly once. An Euler circuit is an Euler path which starts and stops at the same vertex. Our goal is to find a quick way to check whether a graph (or multi graph) has an Euler path or circuit.

hope it helps

4 0

2 years ago

Read 2 more answers

The sum of the measures of the angles is 180. The sum of the measures of the second and third angles is two times the measure of

grigory [225]

Step-by-step explanation:

Let the first angle be $a$ degrees

Let the second angle be $b$ degrees

Let the third angle be $c$ degrees

It is given that sum of angles is $180$ degrees.

so, $a+b+c=180$ ...(i)

It is given that sum of the measures of the second and third angles is two times the measure of the first angle.

$b+c=2\times a$ ...(ii)

It is given that the third angle is 26 more than the second.

$c=26+b$ ...(iii)

using (ii) and (iii),

$b+b+26=2a$

$b+13=a$

using (i),(ii) and (iii),

$a+b+c=a+a-13+26+b=a+a-13+26+a-13=3a$

$3a=180$

$a=60$

$b=a-13=60-13=47$

$c=26+b=26+47=73$

3 0

3 years ago

Iris wants to buy sneakers at $15 each and high heels at $30 each. Write an algebraic expression to find the total cost of the s

kogti [31]

Answer: 30y + 15x

If x is for sneakers, and y is for high heels, plug 15 in for a and 30 in for b. This means that x is how many sneakers she buys, and y is how many high heels she buys. The equation altogether represents the total amount of her purchases.

5 0

2 years ago

Can someone simplify pls

algol [13]

we are given to simplify

$\\ \ (x^6y^5)(5xy^2)(-6x^4)\\ \\$