Quadratic Standard Vertex

A parabola has a vertex at (-1.5,12.5) and passes through (0,8). Solve for "a" and write the equation in vertex form.

Formula: f(x) = a(x - h)² + k

• y = -1.5(12.5 - 8)²

• y = 2(x + 0)² + 8

• y = -2(x + 1.5)² + 12.5

• y = 8(x + 1.5)² - 12.5

• None of the above

Given the equation above, which of the following statements is FALSE?

• The graph opens upward.

• The vertex is at (7, 4).

• The parabola crosses the x-axis twice.

• The standard form is y= 2x² - 28x + 102.

• The axis of symmetry is x = 7.

Tags

CCSS.HSF-IF.C.7A

Convert the equation into standard form:

• y = -5x² - 20x - 30

• y = -5x² - 4x - 10

• y = 25x² + 100x + 90

• y = 25x² - 10x - 30

Which answer choice(s) below correctly show(s) an equation in vertex form and in its standard form? (There may be more than 1.)

• y = -3(x + 2)² + 3

  y = -3x² - 12x - 15

• y = 2(x + 5)² + 1

  y = 2x² + 20x + 51

• y = 0.5(x - 3)² - 6

  y = 0.5x² - 3x - 1.5

A parabola has a vertex at (1,6) and passes through (3,-18). Write the equation in vertex form. Formula: f(x) = a(x - h)² + k

• f(x) = 3(x - 1)² - 18

• f(x) = -6(x - 1)² + 6

• f(x) = 6(x - 3)² - 18

• f(x) = -3(x + 1)² - 6

When given 3 or more ordered pairs on a parabola, which of the following is a method you can use to find the equation in standard form?

• Make a table of values. Find the rate of change (slope) and y-intercept.

• On the calculator, use STAT-EDIT to enter the values into L₁ and L₂. Then go to STAT>CALC and choose "QuadReg" (option 5).

• 3 ordered pairs will not give you enough information to find the equation for the parabola.

What information do you need to write an equation in vertex form? Select all that apply.

• an ordered pair anywhere on the parabola

• the coordinates for the vertex

• the formula for standard form

• the formula for vertex form

Convert the equation from vertex form (shown) to standard form:

• y = 9x² - 15x + 21

• y = -3x² - 75x - 4

• y = 9x² + 90x + 221

• y = -3x² - 30x - 79

Your teacher gives you an equation in vertex form. If the "a" value is -3, select the statements below that are true.

• "a" will be -3 in standard form

• "a" represents a vertical compression

• "a" will become 9 in standard form

• the parabola will open downward

• "a" describes the horizontal shift

A parabola has a vertex at (6, 5) and passes through (10, -11). Which equation represents this parabola in vertex form?

Formula: f(x) = a(x - h)² + k

• -11 = a(10 - 6)² + 5

• y = -(10 - h)² + k

• y = -(x - 6)² + 5

• y = (x - 6)² + 5