2.5 Quadratic equations  (Page 6/14)

How do we recognize when an equation is quadratic?

When we solve a quadratic equation, how many solutions should we always start out seeking? Explain why when solving a quadratic equation in the form $a{x}^2+bx+c=0$ we may graph the equation $y=a{x}^2+bx+c$ and have no zeroes ( x -intercepts).

When we solve a quadratic equation by factoring, why do we move all terms to one side, having zero on the other side?

In the quadratic formula, what is the name of the expression under the radical sign $b^2-4ac,$ and how does it determine the number of and nature of our solutions?

Describe two scenarios where using the square root property to solve a quadratic equation would be the most efficient method.

$x^2+4x-21=0$

$x^2-9x+18=0$

$2x^2+9x-5=0$

$6x^2+17x+5=0$

$4x^2-12x+8=0$

$3x^2-75=0$

$8x^2+6x-9=0$

$4x^2=9$

$2x^2+14x=36$

$5x^2=5x+30$

$4x^2=5x$

$7x^2+3x=0$

$\frac{x}{3}-\frac{9}{x}=2$

$x^2=36$

$x^2=49$

${\left(x-1\right)}^2=25$

${\left(x-3\right)}^2=7$

${\left(2x+1\right)}^2=9$

${\left(x-5\right)}^2=4$

$x^2-9x-22=0$

$2x^2-8x-5=0$

$x^2-6x=13$

$x^2+\frac{2}{3}x-\frac{1}{3}=0$

$2+z=6z^2$

$6p^2+7p-20=0$

$2x^2-3x-1=0$