Which figure is a quadrilateral? A triangle. A rectangle. A circle. A line.

The axis of symmetry for the function f(x) = –2x2 + 4x + 1 is the line x = 1. Where is the vertex of the function located?

egoroff_w [7]

Answer:

(1, 3)

Step-by-step explanation:

You are given the h coordinate of the vertex as 1, but in order to find the k coordinate, you have to complete the square on the parabola. The first few steps are as follows. Set the parabola equal to 0 so you can solve for the vertex. Separate the x terms from the constant by moving the constant to the other side of the equals sign. The coefficient HAS to be a +1 (ours is a -2 so we have to factor it out). Let's start there. The first 2 steps result in this polynomial:

$-2x^2+4x=-1$ . Now we factor out the -2:

$-2(x^2-2x)=-1$ . Now we complete the square. This process is to take half the linear term, square it, and add it to both sides. Our linear term is 2x. Half of 2 is 1, and 1 squared is 1. We add 1 into the set of parenthesis. But we actually added into the parenthesis is +1(-2). The -2 out front is a multiplier and we cannot ignore it. Adding in to both sides looks like this:

$-2(x^2-2x+1)=-1-2$ . Simplifying gives us this:

$-2(x^2-2x+1)=-3$

On the left we have created a perfect square binomial which reflects the h coordinate of the vertex. Stating this binomial and moving the -3 over by addition and setting the polynomial equal to y:

$-2(x-1)^2+3=y$

From this form,

$y=-a(x-h)^2+k$

you can determine the coordinates of the vertex to be (1, 3)

5 0

3 years ago

Read 2 more answers

People use water to cook, clean, and drink every day. An estimate of 19.4% of the water used each day is for cooking. If a fam

andreev551 [17]

Answer:

350 gallons

Step-by-step explanation:

100/19.4 = 5.15463917526

Multiply this by 67.9 gallons used for cooking = 350 gallons of water a day per family

5 0

3 years ago

F(x) = 2x^2 − 3x − 5 Part

riadik2000 [5.3K]

Answer: Answer is in the steps..

Step-by-step explanation:

f(x)= $2x^{2}$ - 3x -5

A) To find the x intercepts of a parabola we have to set the whole equation equal zero because the x intercept is when y equal zero in other words where f(x) equal zero.

$2x^{2}$ - 3x - 5 = 0 Now solve using quadratic formula.

x = -b± $\frac{\sqrt{b^2 -4ac } }{2a}$

x = 3 ± $\sqrt{9+40} /2a$

x = 3 ± $\sqrt{49}$ / 2a

x= 3 ± 7 /4

x= -1 or x = 5/2

The x intercepts are (5/2,0) and (-1,0)

B) The graph vertex of the graph of f(x) is going to be at a minimum because the leading coefficient of the function has a positive integer which means the parabola will open up and its vertex will be at the minimum point.

Using the x coordinates we could find their average and find the x coordinate of the vertex.

$\frac{5}{2} + -\frac{1}{1}$ = $\frac{3}{2} / \frac{2}{1}$ = 3/4