What is the vertex of a parabola?

The vertex is the minimum or maximum point of a quadratic curve, calculated as x = -b/(2a).

How is the y-intercept of a function found?

Set x = 0 and solve for y. The constant term represents the point where the curve crosses the Y axis.

LINEAR Functions & Graphs Plotter

Y-Intercept(0, -2)

X-Intercepts (Roots) 2.0

Variable Adjuster

Slope (m)1

-55

Y-Intercept (c)-2

-1010

Functions & Graphs Plotter

GRAPH

A function represents a mathematical rule relating inputs (x) to outputs (y). Plotting these points on a Cartesian coordinate system creates lines or curves that reveal rates of change, vertex peaks, and roots (X-intercepts).

y = mx + c

Whiteboard Solver Steps

Step 1

Function Definition (Linear Line)

We are graphing a linear function representing a straight line: $y = mx + c$ . Here, the slope ( $m = 1$ ) dictates the steepness and direction (positive slope rises from left to right, negative falls), and the constant ( $c = -2$ ) defines the vertical offset.

y = 1x + -2

Step 2

Find Y-Intercept (Vertical Crossing)

The y-intercept represents the point where the line crosses the vertical Y-axis. By substituting $x = 0$ into our linear equation, we find that the line passes through the coordinate $(0, -2)$ .

x = 0 \implies y = 1(0) + -2 = -2

Step 3

Find X-Intercept / Root (Horizontal Crossing)

The x-intercept or root is the point where the line crosses the horizontal X-axis. By setting $y = 0$ and solving for $x$ , we find that the line intersects the X-axis at $x \approx 2$ , corresponding to the coordinate $(2, 0)$ .

y = 0 \implies 0 = 1x + -2 \implies x = -\frac{-2}{1} = 2