Mathematics Middle School

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

Answers

Answer 1

Answer:

The vertex is (2,-16)

Step-by-step explanation:

The given function is [tex]f(x)=(x-6)(x+2)[/tex]

We expand to obtain;

[tex]f(x)=x^2+2x-6x-12[/tex]

[tex]f(x)=x^2-4x-12[/tex]

We complete the squares to obtain;

[tex]f(x)=x^2-4x+(-2)^2-12-(-2)^2[/tex]

[tex]f(x)=x^2-4x+(-2)^2-12-4[/tex]

[tex]f(x)=(x-2)^2-16[/tex]

The vertex form is [tex]f(x)=(x-2)^2-16[/tex]

Comparing this to

[tex]f(x)=a(x-k)^2+k[/tex]

The vertex is (h,k)= (2,-16)

Answer 2

Final answer:

The vertex of the quadratic function f(x) = (x - 6)(x + 2) is found by expressing the function in vertex form. After completing the square, the vertex of the function is determined to be at the point (2, -16).

Explanation:

To find the vertex of the quadratic function f(x) = (x
– 6)(x + 2), we first need to express the function in vertex form, which is y = a(x - h)² + k, where (h, k) is the vertex of the parabola. Multiplying out the factors gives us f(x) = x² - 4x - 12. Completing the square allows us to transform this equation into vertex form.

First, Factor out the leading coefficient (which is 1 in this case, so this step is not needed), and then rewrite the function isolating the terms with x:

f(x) = x² - 4x + ____ - 12 + ____.

We complete the square by finding the value that makes x² - 4x + ____ a perfect square trinomial. This value is (-4/2)² = 4, so we add and subtract 4 inside the function:

f(x) = x² - 4x + 4 - 12 - 4.

Now we have f(x) = (x - 2)² - 16. Thus, the vertex form of the function is y = (x - 2)² - 16, and the vertex of the parabola is at the point (2, -16).

Related Questions

What graph represents a reflection of abc over the line x=0

Answers

Answer: D

Step-by-step explanation: APEX

Answer:

The correct option is D)

Step-by-step explanation:

line x = 0 is y-axis (vertical line)

When graph is reflected along y-axis so, it will be in second quadrant.

so, the graph which satisfying these condition is only option D)

in which c ordinate are A has (-1,1) ,B has (-4,1) and C has (-3,3)

Hence, the correct option is D)

Evaluate 3/2y - 3 + 5/3z when y=6 and z=3

Answers

Answer: 11

Step-by-step explanation:

3/2(6) - 3 + 5/3(3)= 11

A triangular prism was sliced parallel to its base. What is the shape of the cross section shown in the figure?

a triangle that has the same dimensions as either base of the prism
a triangle that does not necessarily have the same dimensions as either base of the prism
a parallelogram that is not a rectangle
a rectangle

Answers

Answer:

The answer is a rectangle.

Step-by-step explanation:

A triangular prism was sliced parallel to its base. What is the shape of the cross section shown in the figure?

The answer is rectangle. If the base is a rectangle and we slice it parallel to the base in the same direction as the base, we will get smaller and smaller rectangles with each slice.

This can be clear with the picture attached. If we slice parallel to rectangular base, the cross section will be a rectangle.

Lola measures three buttons for a shirt she’s making. One button is 1/8, 3/8 and 1/4 inch. The button hole is 2/6 of an inch. Which will fit ? Explain

Answers

Answer:

3/8

Step-by-step explanation:

That's the only one bigger than 2/6, any smaller will fall out as it's a button. You'd twist it sort of in half to get it in the hole, therefore, 3/8 is the only button that will fit.

I'm not sure if this is correct but this is how I'd go about it :)

Which expression simplifies 2/5 ? A) (-1/10)-(-1/2) B) (-1/10)+(-1/2) C) (-1/10)×(-1/2) D) (-1/10)÷(-1/2)

Answers

[tex]\bf -\cfrac{1}{10}-\left( -\cfrac{1}{2} \right)\implies -\cfrac{1}{10}+\cfrac{1}{2}\implies \stackrel{\textit{using the LCD of 10}}{\cfrac{-(1)1~~+~~(5)1}{10}}\implies \cfrac{-1+5}{10} \\\\\\ \cfrac{4}{10}\implies \stackrel{simplified}{\cfrac{2}{5}}[/tex]

the 7 represents how many times the value of the 7 in 78

Answers

Answer: 11 times

Step-by-step explanation:

the graph below has the same shape. what is the equation of the graph?

Answers

C; A and B are incorrect because the shift is not vertical, it is horizontal. This is because 3 is in parenthesis or a 'grouping' (same thing if it is in an exponent) and is being modified. Since the graph is being translated down 3 units, D is incorrect since it is a translation up 3 units. The answer is C.

tell whether the angles are complementary or supplementary. then find the value of x

Answers

Hello,

In Q5. Being a straight line the angles are supplementary to each other.

And x = 70°

In Q6.

The angles sum up to 90° , so 25x + 30° = 90

25x = 60°

x= 60°/25 = 2.4°

Hope this helps.

Answer:

see explanation

Step-by-step explanation:

x and 110 form a straight angle and are supplementary, thus

x + 110 = 180 ( subtract 110 from both sides )

x = 70

25x and 30 form a right angle and are complementary, thus

25x + 30 = 90 ( subtract 30 from both sides )

25x = 60 ( divide both sides by 25 )

x = [tex]\frac{60}{25}[/tex] = [tex]\frac{12}{5}[/tex]

Martin can run 1 mile in 7 minutes. What proportions can be written from this information?

Answers

Answer:

[tex]\frac{1}{7}=\frac{3}{21}[/tex]

[tex]\frac{7}{1}=\frac{21}{3}[/tex]

Step-by-step explanation:

Verify each case

case 1) [tex]\frac{1}{7}=\frac{3}{21}[/tex]