Task Sets: Use factoring and completing the square - Common Core Math - HS Functions

Concepts

A quadratic function is written in factored form as $f(x) = 2(x - 4)(x + 1)$ .
Which statement correctly identifies the zeros of $f$ ?

$x = 4$ and $x = -1$

$x = -4$ and $x = 1$

$x = 4$ and $x = 1$

$x = 2$ and $x = 4$

The function $g(x) = (x - 5)^{2} + 3$ is in vertex form $a(x - h)^{2} + k$ .

What is the $x$ -value of the axis of symmetry? Enter a number.

The function $p(x) = -2(x - 1)^{2} + 8$ has a vertex at $(1,\, 8)$ . Does
the vertex represent a maximum or a minimum value of $p$ ?

Maximum, because $a = -2 < 0$ so the parabola opens downward

Minimum, because $a = -2 < 0$ so the parabola opens downward

Maximum, because $k = 8 > 0$

Minimum, because $k = 8 > 0$

Factor $f(x) = x^{2} - 7x + 10$ and identify both zeros.

Zeros at $x = 2$ and $x = 5$

Zeros at $x = -2$ and $x = -5$

Zeros at $x = 1$ and $x = 10$

Zeros at $x = 2$ and $x = -5$

Complete the square to rewrite $f(x) = x^{2} + 6x + 2$ in vertex form
$f(x) = (x - h)^{2} + k$ .

What is the $y$ -coordinate of the vertex (the value of $k$ )?

Complete the square to rewrite $g(x) = x^{2} - 10x + 18$ in vertex form.

What is the $x$ -coordinate of the vertex (the value of $h$ )?

A student rewrites $f(x) = x^{2} + 4x + 1$ by completing the square and
gets $f(x) = (x + 2)^{2} + 1$ . What error did the student make?

The student added $4$ to form the perfect square but forgot to subtract $4$ , so the constant should be $1 - 4 = -3$

The student should have added $2$ instead of $4$ because the formula requires $(b/2)$ , not $b^{2}$

The student made no error; the vertex form is correct

The student should have subtracted $4$ from $x$ inside the parentheses: $(x - 2)^{2}$

Complete the square to find the vertex of $h(x) = -2x^{2} + 8x - 3$ .

What is the maximum value of $h$ (the $k$ -value)?