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## Algebra 1 (Eureka Math/EngageNY)

### Course: Algebra 1 (Eureka Math/EngageNY)>Unit 4

Lesson 8: Topic A: Lessons 8-10: Parabolas intro

# Graphing quadratics in factored form

An example for a quadratic function in factored form is y=½(x-6)(x+2). We can analyze this form to find the x-intercepts of the graph, as well as find the vertex.

## Want to join the conversation?

• What are some real life examples of a parabola (or a quadratic equation)?
• Ballistics with no atmospheric drag (i.e. launching a ballistic missile on the Moon), an orbit with eccentricity of 1, cutting 2 vertex-tangent cones parallel to a slant, astrophysics
• So when you're figuring out the x-values for the intercepts, why doesn't the 1/2 matter?
• The 1/2 will not change the result created by either factor.
Let's say you keep the 1/2 and use it with (x-6)
We use the zero product rule: 1/2 (x - 6) = 0
Distribute: x/2 - 3 = 0
Multiply by 2: x = 6
Notice: this is the same result you would get if you just started with x-6 = 0
Hope this helps.
• Is infinity a number? Or is it just describing all numbers? I'm so confused about this.
• Infinity is not a number, nor does it describe all numbers. Infinity is simply the concept of an arbitrarily large value that does not obey the rules of arithmetic.
• At in the video, why does Mr. Khan place positive 2 in the x place, if the x value was -2? Was that a mistake or something else?
• Hi Sierra,

Mr. Khan put the positive 2 on the x axis to show the average of -2 and 6(using the slope formula). The average shows where to put the parabola.
(1 vote)
• Is there a way to find the sum or the products of the roots?
• You can find the sum of the roots by using -b/a, and the product of the roots, you can use c/a, hope this helps
• How do you know if a parabola is going to be upward or downward opening?
• If the x^2 term is positive, the parabola will open upwards.
If the x^2 term is negative, the parabola will open downwards.
• what if the quadratic doesn't give me the x-intercepts? is there another way to find the two points?
• A parabola
𝑦 = 𝑎𝑥² + 𝑏𝑥 + 𝑐
has its vertex at (−𝑏∕(2𝑎), 𝑐 − 𝑏²∕(4𝑎))

Then we can pick a couple of 𝑥-values fairly close to the line of symmetry and plug them into the equation to find their corresponding 𝑦-values.

– – –

Example: 𝑦 = −3𝑥² + 6𝑥 − 7

The vertex is (−6∕(2 ∙ (−3)), −7 − 6²∕(4 ∙ (−3))) =
= (1, −4)

Picking 𝑥 = 0 ⇒ 𝑦 = −7,
so (0, −7) is a point on the parabola, and since the parabola is symmetric around 𝑥 = 1, we know that (2, −7) is also a point on the parabola.

Similarly, (−1, −16) and (3, −16) are also points on the parabola, and now I'd say we have enough information to draw a decent representation of the parabola.
• What are some real life examples of a parabola
• Can a parabola's `vertex` be at an `x-position` that is not the `average` of the 2 `x-intercepts`? In other words, if I have a parabola with `x-intercepts` of 1 and 3, is there ever a case where the parabola's `vertex` be at an `x-position` of 2.5, rather than 2?