All Precalculus Resources
Which could be the equation for this graph?
Correct answer:
Write the quadratic function for the graph:
Correct answer:
Explanation:
Because there are no x-intercepts, use the form , where vertex is , so , , which gives
Write the quadratic function for the graph:
Correct answer:
Explanation:
Method 1:
The x-intercepts are . These values would be obtained if the original quadratic were factored, or reverse-FOILed and the factors were set equal to zero.
For , . For , . These equations determine the resulting factors and the resulting function; .
Multiplying the factors and simplifying,
.
Answer: .
Method 2:
Use the form , where is the vertex.
is , so , .
Answer:
Write the equation for the polynomial in this graph:
Correct answer:
Explanation:
The zeros for this polynomial are .
This means that the factors are equal to zero when these values are plugged in for x.
multiply both sides by 2
so one factor is
multiply both sides by 3
so one factor is
so one factor is
Multiply these three factors:
Write the equation for the polynomial shown in this graph:
Correct answer:
Explanation:
The zeros of this polynomial are . This means that the factors equal zero when these values are plugged in.
One factor is
One factor is
The third factor is equivalent to . Set equal to 0 and multiply by 2:
Multiply these three factors:
The graph is negative since it goes down then up then down, so we have to switch all of the signs:
Write the equation for the polynomial in the graph:
Correct answer:
Explanation:
The zeros of the polynomial are . That means that the factors equal zero when these values are plugged in.
The first factor is or equivalently multiply both sides by 5:
The second and third factors are and
Multiply:
Because the graph goes down-up-down instead of the standard up-down-up, the graph is negative, so change all of the signs:
Write the equation for the polynomial in this graph:
Correct answer:
Explanation:
The zeros for this polynomial are . That means that the factors are equal to zero when these values are plugged in.
or equivalently multiply both sides by 4
the first factor is
multiply both sides by 3
the second factor is
the third factor is
Multiply the three factors: