Unit 5 Exam Algebra

What are the coordinates of the vertex of the parabola y = 2(x + 2)^2 ?

(-2, 0) (incorrect)

Find the coordinates of the zeros and the vertex in order to graph the parabola represented by the equation y = −(x−3) (x−7). Which figure shows the zeros, vertex, and parabola graphed correctly?

(3, 0) (5, 4) (7,0)

Edward used completing the square to find the minimum value of the expression x^2 + 2x + 5. Which is the equivalent expression after completing the square?

(x + 1) 2 + 4

Use the equation y = −2x^2 + 6x+8y to complete the following table. Which list of values for y correctly completes the table?

0, 8, 12, 12.5, 12, 8, 0

Which equation shows the correct factors for the quadratic equation 24x^2 − 15 = 54x?

3 (8x^2 − 5) = 54x (incorrect)

Leonard needs to design a mat with an 8-×10-inch8-×10-inch opening for a photo that he is going to frame. He wants the mat to have the same width on all four sides, as shown in the following figure. The combined area of the photo and mat needs to be 224 square inches. The equation that represents the combined area is (2w+8)(2w+10)=224, where w represents the width of the mat around the photo. What should the width of the mat be? Enter your answer as the correct value, including units, like this: 42 meters

3 inches

What are the solutions of the equation x^2 = 25/81 ?

5/9, -5/9

To find the minimum value of the quadratic expression −4x^2 + 8x − 25, Marla used the following steps to complete the square: Did Marla use the correct steps to complete the square?

No, Marla should have factored (x^2 + 8x + 16) as (x − 4)^2 (x − 4)^2 instead of (x + 4)^2 (Incorrect)

Which statements are true about the parabola represented by the equation y = −3x^2 + 18x + 23?

The leading coefficient is negative, so the parabola opens down. The parabola has a maximum.

Stellan, an alien from the planet Tellurango, shoots a flaming projectile straight up into the air from the edge of a cliff that is 28 meters high. According to the laws of physics on his planet, the height of the projectile, h, after t seconds is modeled by a quadratic equation. The projectile reaches a maximum height of 64 meters after 6 seconds, and the projectile is airborne for 14 seconds. In other words, after 14 seconds, the projectile has a height of 0 meters because it is on the ground. What is the vertex form of the quadratic equation that represents the height, h, of the projectile after t seconds?

h(t) = -(x - 6)^2 + 64

Justin launches a water balloon vertically from a platform on his roof. The height of the balloon (in feet) is represented by the equation h = −16t^2 + 32t + 48, where t is the time (in seconds) after he launches the water balloon. What is the maximum height of the water balloon? How long does it take the water balloon to reach its maximum height?

time to get to the maximum height = 1 sec h max = 64 feet

Factor the quadratic expression in the equation y = 2x^2 + 8x − 154 and find the zeros of the equation. Then use the zeros to find the line of symmetry of the parabola represented by the equation. What is the equation for the line of symmetry of the parabola represented by the equation y = 2x^2 + 8x− 154?

x = -2

Solve the quadratic equation x^2 + 3x − 10 = 0 by completing the square. What is the solution, or what are the solutions, to the equation?

x = 2, -5

What are the solutions of the equation (x − 8)^2 = 144?

x = 20, -4