Quadratic Forms

If I wanted the roots of a Quadratic equation which form of the Quadratic would I want to use if I didn't want to graph the parabola? Explain your thinking.

Answer explanation

The best form of the Quadratic equation to use would be the Intercept Form since the roots are used to create the factors that are being multiplied.

Tags

CCSS.HSA.REI.B.4

If I want the vertex of a Quadratic equation which form of the Quadratic equation would be the most useful? Explain your thinking.

Answer explanation

The best Quadratic equation form to use to get the vertex of a parabola is the Vertex form, since the vertex is used to create the Quadratic equation.

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Which Quadratic form would be the best to use if I am trying to find the Axis of Symmetry? Explain your thinking.

Answer explanation

Since we have already talked about all three forms of the Quadratic equation we know how to find the axis of Symmetry for all three. For Standard form we can use $x=\ -\frac{b}{2a}$ . For Intercept form we can find the halfway point between the roots. And the easiest would be to use the Vertex form because "h" is the AOS.

Tags

CCSS.HSA.REI.D.10

Which is the best form to use if I am trying to find the y-intercept? Explain your thinking.

Answer explanation

The best quadratic form to use would be the Standard form. Because when we plug in x = 0 we automatically get the y-intercept.

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.10

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Which Quadratic form should I pick if I want to find the vertex at (-7,-1).

• y = x² + 14x + 48

• y = (x + 7)² - 1

• y = (x + 6)(x + 8)

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Which Quadratric form should I use if I want the roots of a given Quadratic equation without graphing it?

• y = (x - 1)² - 9

• y = x² - 2x - 8

• y = (x + 2)(x - 4)

Tags

CCSS.HSA-REI.B.4B

Which of the following is Standard Form?

• $y=ax^2+bx+c$

• $y=a\left(x-p\right)\left(x-q\right)$

• $y=a\left(x-h\right)^2+k$

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Which of the following is Vertex Form?

• $y=ax^2+bx+c$

• $y=a\left(x-p\right)\left(x-q\right)$

• $y=a\left(x-h\right)^2+k$

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.IF.C.8

What is an equation of a parabola with the vertex of  $\left(-2,-4\right)$  ?

•  $y=-\left(x+2\right)^2-4$  

•  $y=\frac{3}{2}\left(x-2\right)^2+4$  

•  $y=\frac{3}{2}\left(x-2\right)^2-4$  

•  $y=\left(x+2\right)^2+4$  

Tags

CCSS.HSA.CED.A.2

Which of the following is Intercept (Factored) Form?

• $y=ax^2+bx+c$

•  $y=a\left(x-r_1\right)\left(x-r_2\right)$ 

• $y=a\left(x-h\right)^2+k$

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3