Homework: Graphing Quadratics

Which equation is Vertex Form?

• y=ax²+bx+c

• y=a(x-h)²+k

Answer explanation

The vertex form of a quadratic equation is given by y = a(x-h)^2 + k, where (h, k) represents the vertex of the parabola. This form is useful for easily identifying the vertex and the axis of symmetry. The other option, y = ax^2 + bx + c, is the standard form of a quadratic equation, not the vertex form.

Tags

CCSS.HSA.SSE.B.3

Which equation is in Standard Form?

• y=a(x-h)²+k

• y=ax²+bx+c

Answer explanation

The question asks for the equation in Standard Form. The correct choice is y=ax^2+bx+c, which represents a quadratic equation in Standard Form. The other option, y=a(x-h)^2+k, represents the Vertex Form of a quadratic equation.

Tags

CCSS.HSA.SSE.A.2

What is the vertex of this quadratic equation?

y = 2(x + 2)² + 5

• (-2,5)

• (2,5)

• (5,-2)

• (-5,-2)

Answer explanation

The vertex of a quadratic equation in the form y = a(x-h)^2 + k is given by the point (h, k). In this case, the equation is y = 2(x + 2)^2 + 5, so the vertex is (-2, 5), which is the correct choice.

Tags

CCSS.HSA.REI.B.4

CCSS.HSA.REI.D.10

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

What is the axis of symmetry?
f(x) = x² - 8x + 15.

• x = -4

• x = 4

• y = 4

• y = -4

Answer explanation

The axis of symmetry for a quadratic function in the form f(x) = ax^2 + bx + c can be found using the formula x = -b / 2a. In this case, a = 1 and b = -8. Plugging these values into the formula, we get x = 8 / 2(1) = 4. Therefore, the axis of symmetry is x = 4.

Tags

CCSS.HSA.REI.D.10

What is the axis of symmetry?
y = 3x² - 6x + 4

• x=1

• x=-6

• x=2

• x=-1

Answer explanation

The axis of symmetry for a quadratic equation in the form y = ax^2 + bx + c can be found using the formula x = -b / 2a. In this case, a = 3 and b = -6. Plugging these values into the formula, we get x = (-(-6)) / (2 * 3) = 6 / 6 = 1. Therefore, the axis of symmetry is x = 1.

Tags

CCSS.HSA.REI.B.4

• (-5, -12)

• (5,-12)

• (5, 12)

• (-5, 12)

Answer explanation

The given equation is in vertex form, which is y = a(x-h)^2 + k. In this case, a = 2, h = 5, and k = 12. The vertex of the parabola is the point (h, k), so the correct answer is (5, 12).

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

• (-2, 16)

• (2, 0)

• (2, 4)

• (-2, 4)

Answer explanation

The given equation is in standard form: y = -x^2 - 4x + 12. To find the vertex, we find x using the formula x=-b/2a. We plug our answer into the equation to find the y-coordinate of the vertex.

• (5, -4)

• (-5, -4)

• (-15, -4)

• (15, -4)

Answer explanation

The given equation is in vertex form: y = a(x-h)^2 + k, where (h, k) is the vertex. In this case, y = 3(x+5)^2 - 4, so the vertex is (-5, -4), which is the correct choice.

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

What is the range of the function graphed above?

• y ≥ -2

• y ≤ 4

• y ≥ 4

• y ≤ -2

Answer explanation

The range of a function is the set of all possible output values (y-values), which are shown on the y-axis. In the given question, the function's range is 'y ≤ 4'. This means that the function's output does not exceed 4 on the y-axis.

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5

Find the y-intercept of y = 2x² - 2x + 1

• 2

• -2

• 1

• -1

Answer explanation

The y-intercept of a function is the y-value where the line crosses the y-axis. This occurs when x=0. Substituting x=0 into the equation y = 2x^2 - 2x + 1, we get y = 1. Therefore, the y-intercept of the given function is 1.

Tags

CCSS.HSA.REI.D.10