Question

Label each statement as true or false regarding the zeros/roots of a quadratic function. The roots zeros of a quadratic function are the same as the factors of the quadratic function. The roots zeros are the spots where the quadratic function intersects with the y-axis. The roots zeros are the spots where the quadratic function intersects with the x-axis. There are not always two roots/zeros of a quadratic function,​

Answer 1

Each statement about the zeros/roots of a quadratic function is assessed, explaining that only certain statements are true, such as roots being the points of intersection with the x-axis and not always having two real roots.

Step-by-step explanation:

Regarding the zeros/roots of a quadratic function, we can assess the true or false nature of each statement as follows:

• The roots (zeros) of a quadratic function are not the same as the factors of the quadratic function. This statement is false. The roots are the values that make the equation equal to zero, and the factors are the binomials that give the roots when set equal to zero.
• The roots (zeros) are the spots where the quadratic function intersects with the y-axis. This statement is false. The y-intercept is where the graph crosses the y-axis, occurring when x=0, but the roots are where the graph crosses the x-axis.
• The roots (zeros) are the spots where the quadratic function intersects with the x-axis. This statement is true. The quadratic equation intersects the x-axis at points where its value is zero, which are the roots.
• There are not always two roots/zeros of a quadratic function. This statement is true. A quadratic function can have one, two, or no real roots depending on the discriminant (b^2 - 4ac).

When solving quadratic equations constructed on physical data, they always have real roots, which are often significant. In the context of two-dimensional (x-y graphing), interpreting the meaning of these roots in physical scenarios, such as the trajectory of a projectile, is crucial to understanding the situation accurately.

Answer 2

True, false, true, true.

Step-by-step explanation:

The roots zeros of a quadratic function are the same as the factors of the quadratic function. This is true because your roots are your factors—>(x-3) is a factor, x=3 is the root.

The roots zeros are the spots where the quadratic function intersects with the y-axis. No! Those are called y-intercepts!

The roots zeros are the spots where the quadratic function intersects with the x-axis. True. X-intercepts are your solutions. (x-3) graphed would the (3,0). That’s a solution.

There are not always two roots/zeros of a quadratic function,​ True. No solution would be when your quadratic doesn’t intersect the x-axis. One solution would be when your vertex would be on the x-axis. Two solutions is when your quadratic intersects the x-axis twice. Can there be infinite solutions? No. It’s either 0, 1, or 2 solutions.