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What is the vertex form of the parabola whose standard form equation is y=5x^2-30x+49

agasfer [191]

Answer:

The vertex is (3,4)

Step-by-step explanation:

To convert a quadratic from

y = a x 2 + b x + c

form to vertex form,

y = a ( x − h ) 2 + k , you use the process of completing the square.

First, we must isolate the x

terms:

y − 49 = 5 x 2 − 30 x + 49 − 49

y − 49 = 5 x 2 − 30 x

We need a leading coefficient of 1

for completing the square, so factor out the current leading coefficient of 2.

y − 49 = 5 ( x 2 − 6 x )

Next, we need to add the correct number to both sides of the equation to create a perfect square. However, because the number will be placed inside the parenthesis on the right side we must factor it by

2

on the left side of the equation. This is the coefficient we factored out in the previous step.

y − 49 + ( 5 ⋅ ? ) = 5 ( x 2 − 6 x + ? )

<- Hint:

62 = 3 ; 3 ⋅ 3 = 9

y − 49 + ( 5 ⋅ 9 ) = 5 ( x 2 − 6 x + 9 )

y− 49 + 45 = 5 ( x 2 − 6 x + 9 )

y − 4 = 5 ( x 2 − 6 x + 9 )

Then, we need to create the square on the right hand side of the equation:

y − 4 = 5 ( x − 3 ) 2

Now, isolate the y term:

y − 4 + 4 = 5 ( x − 3 ) 2 + 4

y − 0 = 5 ( x − 3 ) 2 + 4

The vertex is:

( 3 , 4 )

7 0

3 years ago

If events A and B are independent, what must be true?A.) P(AB) = P(B)

anygoal [31]

Answer:

B.) P(A/B) = P(A)

Step-by-step explanation:

If two events, A and B are independent:

We have that:

$P(A \cap B) = P(A)P(B)$

Conditional Probability

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

Since they are independent:

$P(A \cap B) = P(A)P(B)$

Then

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{P(A)P(B)}{P(A)} = P(B)$

So

$P(B|A) = P(B)$ , or either:

$P(A|B) = P(A)$ , and thus, the correct answer is given by option B.

7 0

3 years ago

What equals 5 in multiplication and -4 in addition

kirill [66]

Answer:

-2 +i
-2 -i

Step-by-step explanation:

There is no pair of real numbers that have a total of -4 and a product of 5. The complex numbers (-2+i) and (-2-i) will meet your requirements.

__

If the numbers of interest are 'a' and 'b', they will be zeros of the quadratic whose factored form is ...

(x -a)(x -b) = 0

Expanding that, we find an opportunity to use the given sum and product numbers:

x² -(a+b)x +ab = 0

x² -(-4)x +5 = 0

Rewriting this in vertex form gives ...

(x² +4x +4) +1 = 0

(x +2)² +1 = 0

We can find the values of x by subtracting 1 and taking the square root.

(x +2)² = -1

x +2 = ±√(-1) = ±i

x = -2±i

The two numbers of interest are -2+i and -2-i.

4 0

2 years ago

Is - 7/8 or - 1/15 larger

Anna35 [415]

Answer:

-1/15 because it is closer to zero on the negative half of a number line.

7 0

3 years ago

Read 2 more answers

PLS ANSWER FAST ! 100 POINTS + BRAINLIEST IF CORRECT ! TSM

denis-greek [22]

Answer:

36 inches by 18 inches

Step-by-step explanation:

We are dilating by a factor of 3, which means the image gets larger

12*3 = 36 inches

6 *3 =18 inches

The new figure would be 36 inches long by 18 inches high

5 0

3 years ago

Read 2 more answers