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Geometry | Unit 6 | Lesson 7: Distances and Parabolas | Practice Problems

Authored by Illustrative Mathematics

Mathematics

6th Grade

Geometry | Unit 6 | Lesson 7: Distances and Parabolas | Practice Problems
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9 questions

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1.

OPEN ENDED QUESTION

3 mins • 1 pt

The point \((6,y)\) is the same distance from \((4,1)\) as it is from the \(x\)-axis. What is the value of \(y\)?

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2.

MULTIPLE SELECT QUESTION

30 sec • 1 pt

A parabola is defined as the set of points the same distance from \((6,2)\) and the line \(y=4\). Select all points that are on this parabola.

(1,-2)

(2,-1)

(6,2)

(7,3)

(8,2)

3.

OPEN ENDED QUESTION

3 mins • 1 pt

Compare and contrast the parabolas with these definitions. parabola A: points that are the same distance from \((0,4)\) and the \(x\)-axis parabola B: points that are the same distance from \((0,\text-6)\) and the \(x\)-axis

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4.

OPEN ENDED QUESTION

3 mins • 1 pt

Find the center and radius of the circle represented by the equation \(x^2+y^2-8y+5=0\).

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5.

MULTIPLE SELECT QUESTION

30 sec • 1 pt

Match each expression with the value needed in the box in order for the expression to be a perfect square trinomial.

2: 49

B: \(x^2 -\frac12 x + \boxed{\phantom{3}}\)

3: 25

A: \(x^2 + 14x + \boxed{\phantom{3}}\)

6.

OPEN ENDED QUESTION

3 mins • 1 pt

Write each expression as the square of a binomial.

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7.

OPEN ENDED QUESTION

3 mins • 1 pt

Write an equation of a circle that is centered at \((1,-4)\) with a radius of 10.

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