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lesya [120]
1 year ago
8

Given the vertex of a quadratic function, find the axis of symmetry.

Mathematics
1 answer:
motikmotik1 year ago
5 0

(i) The equation of the axis of symmetry is x = - 5.

(ii) The coordinates of the vertex of the parabola are (h, k) = (4, - 18). The x-value of the vertex is 4.

(iii) According to the <em>vertex</em> form of the <em>quadratic</em> equation, the parabola opens down due to <em>negative</em> lead coefficient and has a vertex at (2, 4), which is a <em>maximum</em>.  

<h3>How to analyze and interpret quadratic functions</h3>

In this question we must find and infer characteristics from three cases of <em>quadratic</em> equations. (i) In this case we must find a formula of a axis of symmetry based on information about the vertex of the parabola. Such axis passes through the vertex. Hence, the equation of the axis of symmetry is x = - 5.

(ii) We need to transform the <em>quadratic</em> equation into its <em>vertex</em> form to determine the coordinates of the vertex by algebraic handling:

y = x² - 8 · x - 2

y + 18 = x² - 8 · x + 16

y + 18 = (x - 4)²

In a nutshell, the coordinates of the vertex of the parabola are (h, k) = (4, - 18). The x-value of the vertex is 4.

(iii) Now here we must apply a procedure similar to what was in used in part (ii):

y = - 2 · (x² - 4 · x + 2)

y - 4 = - 2 · (x² - 4 · x + 2) - 4

y - 4 = - 2 · (x² - 4 · x + 4)

y - 4 = - 2 · (x - 2)²

According to the <em>vertex</em> form of the <em>quadratic</em> equation, the parabola opens down due to <em>negative</em> lead coefficient and has a vertex at (2, 4), which is a <em>maximum</em>.  

To learn more on quadratic equations: brainly.com/question/1863222

#SPJ1

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FrozenT [24]

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<h3>What are the condition for Correlation?</h3>

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This is achieved when there's uniformity in slopes x and y.

4. Weak Correlation

This is achieved when there are no uniforms in slopes x and y

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8 0
2 years ago
Which inequality is a true statement?
nordsb [41]

Answer It's A, B, C, and F. Or 1, 2, 3, 5

Step-by-step explanation:

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7 0
3 years ago
How can you use substitution to solve a system of linear equations?
makvit [3.9K]
Step 1:
Solve one of the equations for either x = or y = .
Step 2:
Substitute the solution from step 1 into the other equation.
Step 3:
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Step 4:
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Example 1: Solve the following system by substitution
Substitution Method Example
Solution:
Step 1: Solve one of the equations for either x = or y = . We will solve second equation for y.
solution step 1
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solution step 2
Step 3: Solve this new equation.
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3 years ago
Match each equation with its solution set.
taurus [48]

Answer:

1- The solution of I2x + 5I = 9 is {-7 , 2}

2- The solution of I2x + 7I + 2 = 11 is {-8 , 1}

3- The solution of I5 - xI = 6 is {-1 , 11}

4- The solution of I6x - 8I + 7 = 5 is ∅

5- The solution of Ix + 3I = 12 is {-15 , 9}

6- The solution of Ix - 3I = -12 is ∅

Step-by-step explanation:

* At first lets explain the meaning of IxI = a

- If IxI = a ⇒ then x = a or x = -a

- IxI never give a negative answer, because IxI means the

 magnitude of x is always positive

Ex: I-2I is 2

* Now lets find the solution of each equation

1- ∵ I2x + 5I = 9

∴ 2x + 5 = 9 ⇒ subtract 5 from both sides

∴ 2x = 4 ⇒ divide both sides by 2

∴ x = 2

OR

∴ 2x + 5 = -9 ⇒ subtract 5 from both sides

∴ 2x = -14 ⇒ divide both sides by 2

∴ x = -7

* The solution of I2x + 5I = 9 is {-7 , 2}

2- ∵ I2x + 7I + 2 = 11 ⇒ Subtract 2 from both sides

∴ I2x + 7I = 9

∴ 2x + 7 = 9 ⇒ subtract 7 from both sides

∴ 2x = 2 ⇒ divide both sides by 2

∴ x = 1

OR

∴ 2x + 7 = -9 ⇒ subtract 7 from both sides

∴ 2x = -16 ⇒ divide both sides by 2

∴ x = -8

* The solution of I2x + 7I + 2 = 11 is {-8 , 1}

3- ∵ I5 - xI = 6

∴ 5 -x = 6 ⇒ subtract 5 from both sides

∴ -x = 1 ⇒ divide both sides by -1

∴ x = -1

OR

∴ 5 -x = -6 ⇒ subtract 5 from both sides

∴ -x = -11 ⇒ divide both sides by -1

∴ x = 11

* The solution of I5 - xI = 6 is {-1 , 11}

4- ∵ I6x - 8I + 7 = 5 ⇒ Subtract 7 from both sides

∴ I6x - 8I = -2

- I  I never give negative answer

* The solution of I6x - 8I + 7 = 5 is ∅

5- ∵ Ix + 3I = 12

∴ x + 3 = 12 ⇒ subtract 3 from both sides

∴ x = 9

OR

∴ x + 3 = -12 ⇒ subtract 3 from both sides

∴ x = -15

* The solution of Ix + 3I = 12 is {-15 , 9}

6- ∵ Ix - 3I = -12

- I  I never give negative answer

* The solution of Ix - 3I = -12 is ∅

4 0
3 years ago
How many squares are on the chessboard
natka813 [3]
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That’s is your answer
Thanks jaddan.
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