All Precalculus ResourcesWhich 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: All Precalculus Resources |