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Transcript

  • It has WOW effect.Very WOW.

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  • Make your audience remember the message.

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by angela and xochitl

Quadratic debate project

What is an intercept?

What is a vertex?

Vertex & Intercepts

An intercept, is where a graph touches the x & y axis. Usually when x or y, equal 0.

The vertex is the maximum or minimum value of the parabola.

  • Y-Intercept: Set π‘₯=0 and solve for y
  • X-Intercepts: Set 𝑦=0 This gives π‘₯=𝑝 and π‘₯=π‘ž

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  • Set 𝑦=0 and solve for π‘₯ : 0=π‘Žπ‘₯2+𝑏π‘₯+𝑐
Or you can use the quadratic formula

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  • Use the formula x=p+q/2 and then substitute in the equation to find y

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  • Compare the given equation with y=a(x-h)*+h and identify the value of h and k. (h,k) is the vertex

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  • Use the formula x=-b/2a and then substituing to find y

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...the intercepts...

...the vertex...

how to find...

  • Set x=0 and solve for y :
y=a(0)2+b(0)+c=c The y-int is (0,c)

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... in standard form:

... in vertex form:

... in standard form:

... in intercept form:

... in intercept form:

... in vertex form:

Cons

Pros

Intercepts

  • It is easier to find the intercept form equation
  • You know where the line touches the x and y axis
  • It can help you graph the graph more easily
  • It tells us when x and y equal 0

  • It is harder to find the vertex and standard form equations
  • It requires more work to find the equation of the graph
  • Sometimes there are no x or y intercepts
  • You have to find the vertex to graph

Cons

Pros

Vertex

  • Represents the maximum or minimum value of the parabola.
  • It is a key point to graph the parabola.
  • It is the axis of symmetry for the parabola
  • You need to find it to graph the parabola

  • The vertex alone doesn't provide information about the width or steepness of the parabola
  • Without the x- and y-intercepts, you may not fully understand where the parabola lies in relation to the axes
  • Different parabolas can share the same vertex but have different shapes or orientations

Intercepts

Vertex

Arguments

Intercepts are better, because they give you more information. It can help you find where the y and x intercept with the axis. Though it might take a bit more work to find the full equation it is easier to sketch the graph. Knowing this you can graph more easily and find the equation.

The vertex reveals the parabola's highest or lowest point. This simplifies calculations and helps you quickly understand its shape and direction. In many real-world applications, like physics or engineering, the vertex is often more important than the intercepts.

In basketball, when a player shoots the ball, its path forms a parabola. The vertex shows the highest point the ball will reach. By understanding where the vertex point should be, the player can shoot more accurately and increase the chances of making the basket.

vertex - basketball

Real-world application

In a job the x is the amount of hours worked and y is the amount earned. The x-intercept would be (0,0). The y-intercept would also be (0,0) since we start with no money.

intercepts - a job