7. Quadratics

7.01 Key features of quadratic functions

7.02 Solving quadratic equations by factoring

7.03 Solving quadratic equations using square roots

Investigation: Deriving the quadratic formula

7.04 Complex numbers

7.05 The discriminant and the quadratic formula

[Deprecated] Solve quadratic equations using the quadratic formula

7.06 Transformations of quadratics

7.07 Graphing quadratic functions

7.08 Quadratics in factored form

7.09 Quadratic functions and technology

7.10 Quadratics in vertex form

7.11 Applications of quadratic functions

7.12 Systems of linear and quadratic equations

United States of America NC

Math 2

7.10 Quadratics in vertex form

Interactive practice questions

What is the point $\left(h,k\right)$(h,k) on the parabola defined by the equation $y=a\left(x-h\right)^2+k$y=a(x−h)2+k?

$y$y-intercept

A

Vertex

B

Axis of symmetry

C

$x$x-intercept

D

Easy

< 1min

For an equation of the form $y=a\left(x-h\right)^2+k$y=a(x−h)2+k, what is the least number of points required to graph the curve?

Easy

< 1min

Consider the equation $y=\left(x+1\right)^2$y=(x+1)2.

Easy

3min

Consider the quadratic function $f\left(x\right)=\left(x-3\right)^2$f(x)=(x−3)2.

Easy

2min

Outcomes

NC.M2.A-SSE.3

Write an equivalent form of a quadratic expression by completing the square, where a is an integer of a quadratic expression, ax^2 + bx + c, to reveal the maximum or minimum value of the function the expression defines.

NC.M2.F-IF.7

Analyze quadratic, square root, and inverse variation functions by generating different representations, by hand in simple cases and using technology for more complicated cases, to show key features, including: domain and range; intercepts; intervals where the function is increasing, decreasing, positive, or negative; rate of change; maximums and minimums; symmetries; and end behavior

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