Solve each equation:
${n^2} + n = 90$
$3{b^2} = 12b - 12$
$x^3 = 4x^2 + 5x$
${a^4} - 8{a^2} - 9 = 0$
$(x - 2)(x + 4)(x - 9)(x) = 0$
$(x + 2)(x - 1) = 4$
Find the vertex and zeros of each
parabola:
$y = x^2 - 6x - 16$
$y = 2x^2 - 7x - 4$
$y = - {x^2} - 10x - 25$
$y = {x^2} - 64$
Find the dimensions of a rectangle with area 24 square feet if its length is 2 feet greater than twice its width.
The graph of a quadratic function intersects the $x$-axis at 0 and 8. Find equations for two different parabolas that fit this description.
Find where the parabola $y = {x^2} + 1$ intersects the line $y = x + 3$.
Which of these two equations represents a vertical stretch
3 about the $x$-axis, then a vertical shift of 4, and which
represents a vertical shift of 4, then a vertical stretch of
3 times away from the $x$-axis?
$y = 3{x^2} + 4$ vs. $y = 3({x^2} + 4)$
Use the idea of transformations to find an equation for each parabola:
Vertex at (3,1), also goes through (4,2) and (5,5)
Vertex at (3,1), also goes through (4,-1) and (5,-7)
Vertex at (0,-1), also goes through (-1, -2) and (1,-2)
Vertex at (0,0), also goes through (1,5) and (2, 20)
Describe the graph of the line $y = (x + 1) - 3$ as a transformation of the line $y = x$ in TWO DIFFERENT WAYS.
Determine the value of $a$ such that (3, 108) is on the graph of $y = a{x^2}$.
Determine two values of $h$ such that (-3,4) is on the graph of $y = {(x - h)^2}$
Find the exact solution of each equation:
$x^2 - 6x + 5 = 10$
$2x^2 - 9x - 5 = 0$
${x^2} + 14x = 42$
A parabola has equation $y = {(x + 3)^2} - 4$. Find the $x$-intercepts, the $y$-intercept, and the vertex.
A parabola has equation
How do you know that 5.656854249 can’t really be $\sqrt {32} $?
Another way to write the quadratic
formula is $x = \frac{{ - b}}{{2a}} \pm \frac{{\sqrt {{b^2} -
4ac} }}{{2a}}$
Why is that equivalent to the form you’re more familiar with?
In terms of $a$, $b$, and $c$, how far apart are the two zeroes of the equation $y = ax^2 + bx + c$?