Vertex/Axis of Symmetry for a^2-a+6

Find the vertex, vertex form, and axis of symmetry for a^2-a+6 a = 1, b = 1, c = 1 Use the formula rule. Our equation coefficients are a = 1, b = 1 h = Axis of Symmetry h = -0.5Axis of Symmetry

Vertex/Axis of Symmetry for a^2-a+6 MathCelebrity logo Image to Crop

Find the vertex, vertex form, and axis of symmetry for

a^2-a+6

Set up the a, b, and c values:

a = 1, b = 1, c = 1

Vertex of a parabola
(h,k) where y = a(x - h)2 + k

Use the formula rule.

Our equation coefficients are a = 1, b = 1

The formula rule determines h

h = Axis of Symmetry

h  =  -b
  2a

Plug in -b = -1 and a = 1
h  =  -(1)
  2(1)

h  =  -1
  2

h = -0.5  ← Axis of Symmetry

Calculate k

k = ƒ(h) where h = -0.5

ƒ(h) = a2a1

ƒ(-0.5) = a2a1

ƒ(-0.5) = 0.25 - 0.5 + 1

ƒ(-0.5) = 0.75

Our vertex (h,k) = (-0.5,0.75)

Determine our vertex form:

The vertex form is: a(x - h)2 + k

Vertex form = (x + 0.5)2 + 0.75

Final Answer

Axis of Symmetry: h = -0.5
vertex (h,k) = (-0.5,0.75)
Vertex form = (x + 0.5)2 + 0.75

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What is the Answer?

Axis of Symmetry: h = -0.5
vertex (h,k) = (-0.5,0.75)
Vertex form = (x + 0.5)2 + 0.75

How does the Quadratic Equations and Inequalities Calculator work?

Free Quadratic Equations and Inequalities Calculator - Solves for quadratic equations in the form ax2 + bx + c = 0. Also generates practice problems as well as hints for each problem.
* Solve using the quadratic formula and the discriminant Δ
* Complete the Square for the Quadratic
* Factor the Quadratic
* Y-Intercept
* Vertex (h,k) of the parabola formed by the quadratic where h is the Axis of Symmetry as well as the vertex form of the equation a(h - h)2 + k
* Concavity of the parabola formed by the quadratic
* Using the Rational Root Theorem (Rational Zero Theorem), the calculator will determine potential roots which can then be tested against the synthetic calculator.
This calculator has 4 inputs.

What 5 formulas are used for the Quadratic Equations and Inequalities Calculator?

y = ax2 + bx + c
(-b ± √b2 - 4ac)/2a
h (Axis of Symmetry) = -b/2a
The vertex of a parabola is (h,k) where y = a(x - h)2 + k

For more math formulas, check out our Formula Dossier

What 9 concepts are covered in the Quadratic Equations and Inequalities Calculator?

complete the squarea technique for converting a quadratic polynomial of the form ax2 + bx + c to a(x - h)2 + kequationa statement declaring two mathematical expressions are equalfactora divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n.interceptparabolaa plane curve which is approximately U-shapedquadraticPolynomials with a maximum term degree as the second degreequadratic equations and inequalitiesrational rootvertexHighest point or where 2 curves meet

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