1.2 Graphs of Equations

Solution/solution point

An ordered pair (a,b) ___ of an equation is x and y when the substitutions x = a and y = b result in a true statement.

The Point-Plotting Method of Graphing

1. Solve for one variable

2. make an x,y and (x,y) chart

3. plot points

4. connect dots

quadratic equation

y = ax² + bx + c

zeros (roots)

Solution points of an equation that as either the 𝑥-coordinate or the 𝑦-coordinate

intercepts

They are the points at which the graph intersects or touches the 𝑥- or 𝑦-axis

To find 𝑥-intercepts,

let 𝑦 be zero and solve the equation for 𝑥 (b,0)

To find 𝑦-intercepts,

let 𝑥 be zero and solve the equation for 𝑦 (0,b)

symmetry with respect to the x-axis

whenever (x,y) so is (x,-y)

symmetry with respect to the y-axis

whenever (x,y) so is (-x,y)

Symmetric with respect to the origin

whenever (x,y) so is (-x,-y)

An algebraic test with an equation is symmetric with respect to the 𝑥-axis

when replacing 𝑦 with -𝑦 yields an equivalent equation.

An algebraic test with an equation is symmetric with respect to the y-axis

when replacing x with -x yields an equivalent equation.

An algebraic test with an equation is symmetric with respect to the origin

when replacing x with -x and 𝑦 with -𝑦 yields an equivalent equation.

standard form of the equation of a circle

r² = (x-h)² + (y-k)²

Center of circle

(h, k) follow minus (-) signs

radius of circle

= r

Circle formula with r and center at origin

x² + y² = r²

To find ℎ and 𝑘 from the standard form

rewrite one or both of the quantities in parentheses

h+1 = h - (-1)