20 terms

What happens to the parabola if a>0?

The parabola opens up

What happens to the parabola if a<0?

The parabola opens down

What happens to the parabola if lal >1?

The parabola is narrower than y=x²

What happens to the parabola if lal <1?

The parabola is wider than y=x²

In the standard form equation, what variable represents the y-intercept?

c

What is the graphing shortcut?

1-3-5

What is the difference between quadratics in vertex form and quadratics in standard form?

Vertex: y = a(x - h)²+k {5.1}

Standard: y = ax² + bx + c {5.2}

Standard: y = ax² + bx + c {5.2}

How do you find the Value of a quadratic in Standard form?

First, find the x-value (-b/2a), then plug it in the quadratic equation. If the [a] is positive in the equation, it will have a minimum value; if it is negative, it will have a maximum value.

How do you change the equation, f(x) = 3(x + 2)^2 - 8 in standard form?

1. Square Root

~ f(x) = 3(x + 2)^2 - 8

~ f(x) = 3(x + 2)(x + 2) - 8

2. FOIL

~ f(x) = 3(x + 2)(x + 2) - 8

~ f(x) = 3(x^2 + 2x + 2x + 4) - 8

3. Distribute

~ f(x) = 3(x^2 + 2x + 2x + 4) - 8

~ f(x) = 3x^2 + 6x + 6x + 4 - 8

4. Add Terms

~ f(x) = 3x^2 + [6x + 6x] + [4 - 8]

~ f(x) = 3x^2 + 12x - 4

~ f(x) = 3(x + 2)^2 - 8

~ f(x) = 3(x + 2)(x + 2) - 8

2. FOIL

~ f(x) = 3(x + 2)(x + 2) - 8

~ f(x) = 3(x^2 + 2x + 2x + 4) - 8

3. Distribute

~ f(x) = 3(x^2 + 2x + 2x + 4) - 8

~ f(x) = 3x^2 + 6x + 6x + 4 - 8

4. Add Terms

~ f(x) = 3x^2 + [6x + 6x] + [4 - 8]

~ f(x) = 3x^2 + 12x - 4

When would the parabola open upward?

If [a] is positive

When does a quadratic function have a minimum value?

When the function opens up

What is the formula to finding the axis of symmetry and the x value?

x= -b/2a

How do you tell whether the quadratic function has minimum value or maximum value?

If [a] in the function is a negative number, then the parabola will curve down. The function has a minimum value when [a] is positive. It has a maximum value when [a] is negative.

If the curve points down it has a what value?

Minimum value

If |a|>1, would the parabola be wider or narrower than the parent function?

Narrower

What is the standard form equation?

ax²+bx+c

In standard form, if a is less than 0, which way does the parabola open up?

The parabola opens down if the a is negative.

In standard form, can a = zero

No

If the curve points down will it have a maximum or a minimum?

It will have a maximum value

2x²+x+2 has a ______________________ value

Minimum value