Quadratics Review

Which of these quadratics is in standard form?

Answer explanation

The standard form of a quadratic is y = ax^2 + bx + c. The correct choice, y = 3x^2 + 7x - 1, is in this form. The other options are either rearranged or in vertex form.

Which of the following equations is a quadratic equation in vertex form?

Answer explanation

The equation y=(x-1)^2+5 is in vertex form, which is y=a(x-h)^2+k, where (h,k) is the vertex. The other options are in standard form.

Identify the quadratic equation that is not in standard form.

Answer explanation

The equation y=(x+3)^2-4 is in vertex form, not standard form. Standard form is typically written as y=ax^2+bx+c, which the other options follow.

Which of these expressions represents a quadratic function in factored form?

Answer explanation

The expression y=(x-2)(x+3) is in factored form, showing the roots of the quadratic function. The other options are in standard form, not factored form.

• (-1, -4)

• (-2, -3)

• (-1, 0)

• (0, -4)

Answer explanation

The vertex form of a parabola is given by y = a(x-h)^2 + k, where (h, k) is the vertex. Here, h = -1 and k = -4, so the vertex is (-1, -4). Thus, the correct answer is (-1, -4).

• (2, 3)

• (3, 2)

• (-2, 3)

• (2, -3)

Answer explanation

The vertex form of a parabola is given by y = a(x-h)^2 + k, where (h, k) is the vertex. Here, h = 2 and k = 3, so the vertex is (2, 3). Thus, the correct answer is (2, 3).

Which of these expressions is a quadratic function in vertex form?

Answer explanation

The expression y=(x+4)^2-5 is in vertex form, which is y=a(x-h)^2+k. Here, h=-4 and k=-5 represent the vertex of the parabola. The other options are not in this form.

Identify the quadratic equation that is in factored form.

Answer explanation

The correct choice is y=(x+1)(x-4), which is in factored form. The other options are standard quadratic forms, not factored. Factored form expresses the equation as a product of binomials.

• (2, 3)

• (-3, 2)

• (3, -2)

• (3, 2)

Answer explanation

The vertex form of a parabola is given by y = a(x-h)^2 + k, where (h, k) is the vertex. Here, h = 3 and k = 2, so the vertex is (3, 2). Thus, the correct answer is (3, 2).

• upward

• downward

Answer explanation

The parabola given by y=\frac{1}{2}x^2-8x-10 opens upward because the coefficient of x^2 is positive (\frac{1}{2} > 0). Therefore, the correct answer is upward.

Tags

CCSS.HSF-IF.C.7A