Question

check your understanding 6.1 – intro to graphing intercept form
completing these questions is an opportunity for you to see whether you have understood what happened in your group today.
try them as best as you can first, and ill post the worked out solutions in a few days for you to check your work.
multiply each of the following binomials.

1. $(3x - 4)(7x - 5)$
2. $(9x + 2)(x + 6)$
3. $(4x - 3)(3x + 11)$
4. $(3x - 10)(3x + 10)$
5. $(4x + 5)^2$
6. $(7x - 3)^2$

given the factored form or vertex form of a quadratic function, create a graph and identify the vertex, intercepts, and vertical stretch of the parabola. label your axes with the appropriate scale.

1. $y = (x + 5)(x + 7)$ (with a coordinate grid image)
2. $y = -3(x + 2)(x - 6)$ (with a coordinate grid image)
3. $y = \frac{1}{2}(x - 8)(x + 8)$ (with a coordinate grid image)
4. $y = (x + 2)^2 - 4$ (with a coordinate grid image)
5. $y = -3(x + 6)^2 + 3$ (with a coordinate grid image)
6. $y = 2(x - 1)^2 - 8$ (with a coordinate grid image)

Explanation:

Let's solve the first binomial multiplication problem \((3x - 4)(7x - 5)\) using the distributive property (FOIL method).

Step 1: Apply the FOIL method

Multiply the First terms: \(3x \times 7x = 21x^2\)
Multiply the Outer terms: \(3x \times (-5) = -15x\)
Multiply the Inner terms: \(-4 \times 7x = -28x\)
Multiply the Last terms: \(-4 \times (-5) = 20\)

Step 2: Combine like terms

Combine the middle terms \(-15x\) and \(-28x\): \(-15x - 28x = -43x\)

Step 3: Write the final expression

Combine all terms: \(21x^2 - 43x + 20\)

Answer:

\(21x^2 - 43x + 20\)