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2 years ago

Describe the graph of the quadratic from the original y = x^2 .

Mathematics

1 answer:

Citrus2011 [14]2 years ago

4 0

Answer:

a. Narrower

b. Shifts left

c. Opens up

d. Shifts up

Step-by-step explanation:

The original quadratic equation is y = x²

The given quadratic equation is y = 5·(x + 4)² + 7

The given quadratic equation is of the form, f(x) = a·(x - h)² + k

a. A quadratic equation is narrower than the standard form when the coefficient is larger than the coefficient in the original equation

The quadratic coefficient is 5 > 1 in the original, therefore, the quadratic equation is narrower

b. Given that the given quadratic equation has positive 'a', and 'b', and h = -4, therefore, the axis of symmetry shifts left

c. The quadratic coefficient is positive, (a = 5), therefore, the quadratic equation opens down

d. The value of 'k' gives the vertical shift, therefore, the given quadratic equation with k = 7, shifts up.

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3 years ago

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mihalych1998 [28]

Answer:

$f(x)=5(x-2)^{2}+6$

Step-by-step explanation:

we have

$f(x)=5x^{2} -20x+26$

This is the equation of a vertical parabola open upward

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The equation of a vertical parabola in vertex form is equal to

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Convert the given function to vertex form

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$f(x)=5(x^{2} -4x+4)+6$

Rewrite as perfect squares

$f(x)=5(x-2)^{2}+6$ ------> equation in vertex form

The vertex is the point (2,6)

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3 years ago

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3 years ago

Which graph represents the function f(x) = (x – 3)2?

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C) The third graph.

Step-by-step explanation:

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2 years ago

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You start driving north for 24 miles, turn right, and drive east for another 10 miles. At the end of driving, what is your strai

yawa3891 [41]

Answer:

26 miles

Step-by-step explanation:

Given: 24 miles drive to north.

10 miles drive to east.

Driving pattern form a right angle triangle, which has three leg including straight line distance from starting point (hypotenous).

Now, using Pythogorean theoram to find straight line distance from starting point.

h²= a²+b²

Where, h is hypotenous

a is opposite leg

b is adjacent leg.

⇒h²= $24^{2} + 10^{2}$

⇒ $h^{2} = 576+100$

⇒ $h^{2} = 676$

Taking square root on both side, remember; √a²= ±a

⇒ $h=\sqrt{676}$

∴ $h= \pm 26$

Ignoring -26 as distance cannot be negative.

Hence, 26 miles is the straight line distance from starting point.

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3 years ago