Forms Quadratic Equations

Identify the form of the equation

• Standard Form

• Factored Form

• Vertex Form

Which of the following shows
f(x) = x² - 8x + 1
written in vertex form?

• f(x) = (x - 4)² - 15

• f(x) = (x - 4)² + 17

• f(x) = (x - 4)² - 17

• f(x) = (x - 4)² + 65

Which equation could be the equation of the graph?

• y = -(x-1)(x-3)

• y = (x+3)(x-1)

• y = 2(x+1)(x+3)

• y = -0.5(x+1)(x+3)

Graph the question(hint: use DESMOS or calculator y=).

• Truth

• g(x) has no zeros

• Lie

• g(x) has a vertex at (1,7)

• Truth

• g(x) has a y-intercept at (0,8)

Graph the question(hint: use DESMOS or calculator y=).

• Truth

• m(x) has two negative zeros.

• Lie

• The vertex of m(x) is in quadrant 2.

• Truth

• m(x) has a minimum at 6.

Jackson, Kai, and Abigail are trying to model the path of a ball thrown in the air. Which equation should they use to accurately represent the ball's path, assuming no air resistance?

• y=x²

• y=ax²+bx+c

• y=mx+b

• y=(x-h)² + k

Mason, Kai, and William are playing a game of darts. If the dartboard is represented by a parabolic curve, and the vertex represents the highest possible score, which of the following coordinates would represent the vertex?

• (2, 4)

• (0, 8)

• (3, -1)

• (4, 2)

Identify the vertex.

• (5, 2)

• (5, -2)

• (-5, 2)

• (-5, -2)

Ethan is trying to model the trajectory of a ball thrown in the air using the equation y = x² + 4x + 10. Oliver suggests rewriting the equation in vertex form. How should they rewrite it?

• y = (x + 4)² + 6

• y = (x + 4)² - 6

• y = (x + 2)² + 6

• y = (x + 2)² - 6

Write the following quadratic expression in vertex form.

• y = (x + 4)² - 14

• y = (x + 4)² - 18

• y = (x + 4)² - 6

• y = (x + 4)² + 6