CA 3rd BPB O’Brien Sp09
Recognizing Common Graphs and Equations
Equation Graph How to recognize it Comment
x = a vertical line no y in equation, just x = # vertical lines are not functions
y = b horizontal line no x in equation, just y = # horizontal lines are constant (0 degree) functions
ax + by = c OR y = mx + b oblique line x & y in equation, both to 1st power oblique lines are linear (1st degree) functions
slope = m; y-intercept = b
y = ax2 + bx + c OR y = a(x – h)2 + k parabola highest exponent on x is 2 quadratic (2nd degree) function; x of vertex =
vertex: (h, k); if a > 0, opens up
(x – h)2 + (y – k)2 = r2 circle x & y are both squared center: (h, k); radius: r; circles are not functions
y = ax3 + bx2 + cx + d OR y = a(x – h)3 + k cubic highest exponent on x is 3 cubics are 3rd degree functions
inflection point: (h, k); if a > 0, LH down, RH up
y = ax4 + bx3 + cx2 + dx + e OR y = a(x – h)4 + k quartic highest exponent on x is 4 quartics are 4th degree functions
vertex: (h, k); if a > 0, opens up
half parabola square root with x to 1st power half horizontal parabola with “key” point at (h, k)
half circle square root with x to 2nd power half circle with center at origin & radius = a
cube root cube root looks like horizontal cubic with I.P. at (h, k)
y = a |x – h| + k absolute value absolute value bars v-shape with vertex at (h, k); if a > 0, opens up
piecewise equation is defined in pieces piece with or has solid circle at #
y = ax exponential variable is in the exponent base > 0 & base ≠ 0; J or banana shape
logarithm only equation with log r shape; loge x is written ln x