All categories

3 years ago

What is the vertex of the quadratic function f(x)=(x-6)(x+2)?

Mathematics

1 answer:

Nata [24]3 years ago

4 0

Answer:

(2, -16).

Step-by-step explanation:

(x - 6)(x + 2)

Convert to vertex form:

Expanding the parentheses we have:

x^2 + 2x - 6x - 12

= x^2 - 4x - 12

Completing the square:

= (x - 2)^2 - 4 - 12

= (x - 2)^2 - 16

So the vertex is (2, -16),

You might be interested in

Please help!!!!!!!!!!!!!!!!!

Leokris [45]

Answer:

The domain of a function is defined as the set of x-values for which the function is real and defined. The first alternative is correct

Step-by-step explanation:

3 0

3 years ago

Which statements about limiting reactants are correct? more than one answer may be correct?

Lerok [7]

Where is the question?

3 0

3 years ago

The measure of one of the angles formed by two parallel lines and a transversal is 45°. Is it possible for the measure of any of

liubo4ka [24]

Answer: No

Step-by-step explanation:

Three of the other angles are 45°. The other four are 180° - 45°, which is not 55°. At the intersection of two lines, opposite angles are equal and adjacent angles are complementary, so two adjacent angles add to 180°. Adding a parallel line gives four more angles identical to the first four.

4 0

3 years ago

Brianna is going to a carnival that has games and rides. Each game costs $1.25 and each ride costs $3.75. Brianna spent $18.75 a

maxonik [38]

Answer:

6 games and 3 rides

Step-by-step explanation:

Let the number of games Brianna played be x,

and the number of rides she went on be y.

Total cost for games= 1.25x

Total cost for rides= 3.75y

Since number of games is twice the number of rides,

x= 2y -----(1)

Total costs= cost of games +cost of rides

$18.75= 1.25x +3.75y$

Multiply the whole equation by 4 to remove the decimals:

$75= 5x +15y$

Simplify by dividing the whole equation by 5:

$15 = x + 3y$

Label the equation:

x +3y= 15 -----(2)

Although we can solve these 2 equations by substitution, since the question requires us to graphically solve, we have to graph 2 linear lines.

I will choose 3 points to plot on the graph for each equation:

x= 2y -----(1)

$\begin{tabular}{|c|c|c|c|} \cline{1-4}x & 2(1) = 2&2(2) = 4&2(3) = 6\\ \cline{1-4}y & 1 &2&3\\ \cline{1-4}\end{tabular}$

x +3y= 15 -----(2)

x= -3y +15

$\begin{tabular}{|c|c|c|c|} \cline{1-4}x & -3(1)+15= 12& -3(2)+15= 9& -3(3)+15= 6\\ \cline{1-4}y & 1 &2&3\\ \cline{1-4}\end{tabular}$

Let's plot these points on a graph paper. Then, join them with a straight line for each straight line graph. Please see the attached picture for the graph.

From (1): y= ½x

From (2): 3y= 15 -x

y= 5 -⅓x

From the graph, the solution of the equation is (6,3). The solution is the point on the graph in which the 2 lines intersect.

x- coordinate: 6

y- coordinate: 3

Thus, Brianna played 6 games and went on 3 rides.

8 0

3 years ago

Read 2 more answers

Joshua’s computer loan statement said he would pay $1,244.34 in simple interest for a three-year loan at 12.4%. How much did Jos

rusak2 [61]

Answer: Josh borrowed $ 876 to buy the computer.

Step-by-step explanation:

Formula for simple interest : I = Prt

, where P = principal amount

r= rate of interest ( in decimal)

t=time (in years)

Total amount with simple interest to pay : A = P+I

⇒ A = P +Prt

⇒ A = P(1 +rt) (i)

As per given , A = $1,244.34

r= 12.4% = 0.124

t= 3 years

Now, put these values in (i) , we get

$1244.34=P(1+0.124)^3\\\\\Rightarrow\ 1244.34=P(1.124)^3\\\\\Rightarrow\ 1244.34=P(1.420034624)\\\\\Rightarrow\ P=\dfrac{1244.34}{1.420034624}\\\\\Rightarrow\ P=876.27$

Hence, Josh borrowed $ 876 to buy the computer.

4 0

3 years ago