Menu 416 for Quadratics

Which statement about the quadratic equation is true?

-4.5x² + 72 = 0

• The equation has x = 4 as its only solution

• The equation has no real solutions

• The equation has x = 4 and x = -4 as its only solutions

• The equation has an infinite number of solutions

Tags

CCSS.HSA-REI.B.4B

What is the positive solution to the equation 0 = 1/3x² - 3?

• 3

• -3

• 0

• 1

Tags

CCSS.8.EE.A.2

The total number of seats in an auditorium is modeled by f(x) = 2x² - 6x, where x represents the number of rows of seats. How many rows are there in the auditorium if it has a total of 416 seats?

• 32

• 13

• 20

• 16

What are the solutions to 2(x - 7)² = 32?

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• x = 3 and x = 11

• x = -1 and x = 15

Tags

CCSS.HSA-REI.B.4B

What is the solution set for the quadratic equation x² - 16 = 0?

• {4}

• {-4, 4}

• {256}

• {-256, 256}

Tags

CCSS.HSA-REI.B.4B

The graph of f(x) = x² is transformed to create the graph of h(x) = 2f(x). Which graph best represents f and h?

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The graph of f(x) = x² was transformed to create the graph of g(x) = (x - 7.5)². Which of these describes this transformation?

• A horizontal shift to the right 7.5 units

• A horizontal shift to the left 7.5 units

• A vertical shift down 56.25 units

• A vertical shift up 56.25 units

Quadratic functions q and w are graphed on the same coordinate grid. The vertex of the graph of q is 18 units below the vertex of the graph of w. Which pair of functions could have been used to create the graphs of q and w?

• q(x) = 18x² and w(x) = x²

• q(x) = x² + 18 and w(x) = x²

• q(x) = -18x² and w(x) = x²

• q(x) = x² - 18 and w(x) = x²

Function p is in the form y = ax² + c. If the values of a and c are both less than 0, which graph could represent p?

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The graph of f(x) = x² is shown on the grid.

Which statement about the relationship between the graph of f and the graph of g(x) = 7x² is true?

• The graph of g is narrower than the graph of f.

• The graph of g is wider than the graph of f.

• The graph of g is 7 units below than the graph of f.

• The graph of g is 7 units above than the graph of f.