Unit 6 Test Review

• The vertex is the minimum point of the graph.

• The coordinates of the vertex are (1,-1).

• The graph of the function opens upward.

• The y-intercept is at (0,2).

Answer explanation

The parabola is opening up since a is positive. This means that the vertex is the MINIMUM (or lowest point) of the graph.

Here is the graph of a quadratic function f. Select all equations that could define the function f.

Answer explanation

Vertex form gives us (h, k) of the vertex.

Standard form gives us the vertical intercept of (0, c)

Factored form gives us (0, -a) and (0, -b)

Tags

CCSS.HSF-IF.C.7A

• The y-intercept of the graph is at (0, c).

• The graph has an x-intercept at (c, 0).

• When a < 0 the graph opens downward.

• The graph has two x-intercepts.

• If b = 0, then the vertex is on the y-axis.

Answer explanation

Recall our discussion about the standard form. a tells us if the parabola is open up (+) or open down (-).

c gives us the y-intercept.

NEW FACT, when b is zero the vertex will be on the y-axis.

Tags

CCSS.HSF-IF.C.7A

• Lin's stone

• Clare's stone

• Both hit at the same time

• Cannot be determined

Answer explanation

Remember that the positive x-intercept is the time when the rock hits the water for either child!

• Yes, Clare's stone reached a higher maximum

• No, Clare's stone did not reach a higher maximum

• Cannot determine with the given information

Answer explanation

We are comparing the vertex of either throw. We can find Clare's vertex by substituting the x-value.

• (-2, 4)

• (2, -4)

• (-2, -4)

• (2, 4)

Answer explanation

Recall the vertex form f(x) = a(x - h)^2 + k

h is the x coordinate of the vertex

k is the y coordinate of the vertex

• Minimum value

• Maximum value

Answer explanation

In the vertex form, f(x) = a(x - h)^2 + k

recall that a will determine is the parabola is open up (+) or down (-). If it is open down the vertex is a maximum, and vice versa.

Answer explanation

A vertical shift adds 6 to the k in vertex form!

Mathematical Equivalence

ON

Answer explanation

The useful zero is 10, since this will cause the output to be zero and shows us one of the times that the object is on the ground. The other is irrelevant and doesn't fit the scenario since time won't be negative.

Mathematical Equivalence

ON

Answer explanation

By multiplying the constants (49 and 10) we can find the height where the object was dropped from.