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3 years ago

write a quadratic function that has a graph that contains the following points, (-2, 0), (4, -12), (5,0).

Mathematics

1 answer:

ankoles [38]3 years ago

4 0

Answer:

f(x) = 2x^2 - 6x - 20.

Step-by-step explanation:

(-2, 0) and (5, 0) are 2 zeroes of the function so we can write the function as

f(x) = a(x + 2)(x - 5) where a is a constant.

Now as (4, -12) is a point on the graph:

-12 = a(4 + 2)(4 - 5)

-12 = a * 6 * -1

-6a = -12

a = 2.

So f(x) = 2(x + 2)(x - 5)

f(x) = 2x^2 - 6x - 20.

You might be interested in

The University of Texas at Austin has three times as many students enrolledas the University of Miami. The University of Califor

harina [27]

Answer:

University of Texas has 46,500 students, University of California has 34,000 students and University of Miami has 15,500 students.

Step-by-step explanation:

Represent Texas with T, Miami with M and California with C. With the given information, the following equations were obtained.

T = 3 × M

T – 3M = 0 ………………………….(i)

C = 3,000 + 2 × M

C – 2M = 3,000…………………..(ii)

T + C + M = 96,000…………….(iii)

By rearranging, we have:

1T + 0C – 3M = 0 ………………………….(i)

0T + 1C – 2M = 3,000…………………..(ii)

1T + 1C + 1M = 96,000………….…….(iii)

The Augmented Matrix is:

$\left[\begin{array}{ccc}1&0&-3\\0&1&-2\\1&1&1\end{array}\right]$ $\left[\begin{array}{ccc}T\\C\\M\end{array}\right]$ = $\left[\begin{array}{ccc}0\\3,000\\96,000\end{array}\right]$

Making $\left[\begin{array}{ccc}T\\C\\M\end{array}\right]$ the subject of the formula we have:

$\left[\begin{array}{ccc}T\\C\\M\end{array}\right]$ = $\frac{\left[\begin{array}{ccc}0\\3,000\\96,000\end{array}\right]}{\left[\begin{array}{ccc}1&0&-3\\0&1&-2\\1&1&1\end{array}\right]}$

Let’s say matrix A = $\left[\begin{array}{ccc}1&0&-3\\0&1&-2\\1&1&1\end{array}\right]$ , the inverse of matrix A = $\left[\begin{array}{ccc}\frac{1}{2} &-\frac{1}{2} &\frac{1}{2} \\-\frac{1}{3} &\frac{2}{3} &\frac{1}{3} \\-\frac{1}{6} &-\frac{1}{6} &\frac{1}{6} \end{array}\right]$ is determined by the formula $\frac{Adjoint(A)}{determinant(A)}$ . This can also be computed directly on a scientific calculator.

$\left[\begin{array}{ccc}T\\C\\M\end{array}\right]$ = $\left[\begin{array}{ccc}\frac{1}{2} &-\frac{1}{2} &\frac{1}{2} \\-\frac{1}{3} &\frac{2}{3} &\frac{1}{3} \\-\frac{1}{6} &-\frac{1}{6} &\frac{1}{6} \end{array}\right]$ $\left[\begin{array}{ccc}0\\3,000\\96,000\end{array}\right]$

= $\left[\begin{array}{ccc}46,500\\34,000\\15,500\end{array}\right]$

T = 46,500

C = 34,000

M = 15,500

6 0

4 years ago

Read 2 more answers

5,900 round to the nearest thousand

Karo-lina-s [1.5K]

The answer is six thousand

3 0

3 years ago

2/5 - 1/3 (simplified if possible)

Kipish [7]

Answer:

1/15

Step-by-step explanation:

(1). Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD (Least Common Denominator).

So lets do step one now, the LCD is 15 so we have to make both denominators agree on one number, so 15 is the number both denominators agree on.

Solve:

2*3/5*3 - 1*5/3*5

(2). Complete the multiplication.

6/15 - 5/15

(3). The two fractions now have like denominators so you can subtract the numerators.

6 - 5 / 15 - 15 = 1/15

*Pro tip:

The denominator doesn't change and stays the same. So you don't 

subtract the 15 by 15.

(4). Then you'll get the answer and then if you can simplify then simplify.

The Answer is 1/15, and cannot be simplified.

So the answer is 1/15

Hope this helps!

7 0

2 years ago

Can you help me answer #8 &9?

sukhopar [10]

Answer:

im in 6th grade idk whatt that is

Step-by-step explanation:

3 0

3 years ago

Springfield and Futureland are 750 miles apart. Carmen leaves Springfield traveling toward Futureland at 65 miles per hour. At t

guapka [62]

Answer:

325 miles

Step-by-step explanation:

Their speed of closure is 65 + 85 = 150 mph, so they will cover the 750 mile distance in 750/150 = 5 hours. After that length of time, Carmen will have traveled from Springfield (65 mi/h)·(5 h) = 325 miles to their meeting point.

6 0

3 years ago