Question

My factors for a quadratic are (x + 2)(x - 3), so what would my solutions be for this graph?

Answer 1

The solutions to the quadratic equation formed by the factors (x + 2)(x - 3) are x = -2 and x = 3, representing the points where the quadratic graph intersects the x-axis.

Step-by-step explanation:

The student's question pertains to finding the solutions of a quadratic equation based on its factors. The given factors are (x + 2)(x - 3). To find the solutions, also known as the roots of the equation, we set each factor equal to zero and solve for x. When you have a factor (x + 2),

it implies that one of the solutions is x = -2 since (x + 2) would equal zero at this point. Similarly, for the factor (x - 3), the solution is x = 3 as it makes the (x - 3) term zero. Therefore, for the quadratic equation x² + bx + c = 0 derived from the factors (x + 2)(x - 3), which expands to x² - x - 6 = 0, the solutions are x = -2 and x = 3. These solutions represent where the graph of the quadratic function intersects the x-axis.

For (x + 2) = 0, when we subtract 2 from both sides, we get x = -2.

For (x - 3) = 0, when we add 3 to both sides, we get x = 3.

So, the solutions for this quadratic equation are x = -2 and x = 3.

Answer 2

x = - 2 , x = 3

Step-by-step explanation:

to find the solutions , equate the product of factors to zero , that is

(x + 2)(x - 3) = 0

equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

x - 3 = 0 ⇒ x = 3

the solutions are x = - 2 and x = 3

that is the x- intercepts for the graph are x = - 2 and x = 3