Write equation in standard and vertex form from a graph

What are coordinates of the vertex of a parabola often represented by?

• (x, y)

• (x₂, y₂)

• (h, k)

• (r₂, d₂)

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

y = -3(x + 5)² - 4

Formula: y = ax² + bx + c

• y = 9x² - 15x + 21

• y = -3x² - 75x - 4

• y = 9x² + 90x + 221

• y = -3x² - 30x - 79

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

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

Tags

CCSS.HSA.SSE.A.1

CCSS.HSF.BF.B.3

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

y = 2(x - 7)² + 4

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 = -5(x + 2)² - 10

• 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

Which of the following statements are TRUE?

Select all that apply.

• The "a" value is positive.

• The y-intercept is positive.

• It has two zeros.

• The axis of symmetry is x = 1.

• The vertex is at (0, 5).

Tags

CCSS.HSF-IF.C.7A

Write a quadratic equation given the x intercepts and one other point.

Step 2: Find a.

Now that you know that the factors are (x-6) and (x-8), you must find a. Plug the coordinates of the vertex (7, 1) in for x and y and solve for a.

y = a(x-6)(x-8)

What is the value of a?

• a = 1

• a = -1

• a = 7

• a = -7

Write a quadratic equation given the x intercepts and one other point.

Step 3: Write the equation in factored form.

Now, you know that the factors are (x-6) and (x-8) and a = -1. Write the equation of the graph in factored form.

• -(x-6)(x-8)

• -(x+6)(x+8)

• (x-6)(x+8)

• (x+6)(x-8)

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

Write a quadratic equation given the x intercepts and one other point.

Put the steps together.

1. Find the factors.
2. Solve for a by substituting in the extra point.
3. Write the equation in factored form.

The roots of the function are (-3, 0) and (5, 0).

The point (4, -3) is also on the graph.

• y=4(x+3)(x-5)

• y=3/7(x-3)(x+5)

• y=-3(x-3)(x+5)

• y=3/7(x+3)(x-5)