Create a quadratic equation in standard form that can be solved by either factoring or grouping or by using the quadratic formula.

Question

Then, graph your equation. You can choose to graph by hand, and insert an image of it, OR by using DESMOS (click here for link). If you use DESMOS, copy and paste a link to your graph, DO NOT insert an image if you use DESMOS.

DO NOT use one of the equations from the next problem.

You can choose to do your work on paper and submit via webmail. If you submit via webmail write "Submitted via webmail" in the box below with the date.

You can create up to one additional equation AND graph for extra credit.

(5 points)

9th grade level

Answer 1

Here's a quadratic equation in standard form:

\[ x^2 - 7x + 10 = 0 \]

Solving by Factoring

To factor the equation, we look for two numbers that multiply to +10 (the constant term) and add up to -7 (the coefficient of the linear term).

Those numbers are -5 and -2.

So we can factor the equation as:

\[ (x - 5)(x - 2) = 0 \]

Setting each factor equal to zero gives us:

1. \( x - 5 = 0 \) ⇒ \( x = 5 \)
2. \( x - 2 = 0 \) ⇒ \( x = 2 \)

Solutions

The solutions are \( x = 5 \) and \( x = 2 \).

Graphing the Equation

I created a graph using Desmos. Here's the link to the graph:

Desmos Graph

Extra Credit Equation (Optional)

For extra credit, here’s an additional quadratic equation:

\[ x^2 + 4x + 4 = 0 \]

Factoring this, we get:

\[ (x + 2)(x + 2) = 0 \]

So the solution is:

\( x = -2 \)

You can graph this equation on Desmos as well.

Feel free to use these equations and graphs for your assignment!

Answer 2

all in a simple sentencs

Answer 3

Here’s a quadratic equation: \(x^2 - 7x + 10 = 0\); it factors to \((x - 5)(x - 2) = 0\) with solutions \(x = 5\) and \(x = 2\); you can view the graph here: Desmos Graph.

For extra credit, the equation \(x^2 + 4x + 4 = 0\) factors to \((x + 2)(x + 2) = 0\) with a solution \(x = -2\).