Finding Zeros of Quadratic Functions with Leading Coefficient Greater Than One

This video tutorial teaches how to identify the zeros of a quadratic function by factoring, especially when the leading coefficient is greater than one. It begins with an introduction to the concept of zeros and a review of factoring. The core lesson demonstrates how to rewrite a quadratic function in factored form and find its zeros by setting the factors equal to zero. A general formula for finding zeros in factored form is provided, followed by an example and discussion of common mistakes. The lesson concludes with a summary of the key points.

What is the first step in identifying the zeros of a quadratic function when the leading coefficient is greater than one?

• Rewrite the function in factored form

• Set the function equal to one

• Rewrite the function in standard form

• Graph the function

When rewriting the function 3x^2 + x - 4 in factored form, what are the two factors?

• (x - 4) and (3x + 1)

• (x + 4) and (3x - 1)

• (3x - 4) and (x + 1)

• (3x + 4) and (x - 1)

What is the zero of the function f(x) = x - 3?

• x = 1

• x = -3

• x = 3

• x = 0

How can you verify the zeros of a quadratic function using a graph?

• By checking the vertex

• By checking the slope

• By checking the x-intercepts

• By checking the y-intercepts

In the general form Ax - H and Bx - K, how do you find the zeros?

• X = H / A and X = K / B

• X = -H / A and X = -K / B

• X = A / H and X = B / K

• X = -A / H and X = -B / K

What is a common mistake when identifying zeros from factored form?

• Using the wrong formula

• Not factoring completely

• Ignoring the leading coefficient

• Not substituting back into the original function

If a student finds zeros as -2/5 and -3/2, what should they do to verify?

• Check if these values make the function zero

• Check if these values make the function positive

• Check if these values make the function one

• Check if these values make the function negative