Finding Maximum/Minimum/Intercepts on Calculator

How to generate a quadratic equation and calculate the correlation coefficient using information in a chart

☆*click the "y=" button*→make sure the equation at '/Y₁' is cleared→click the quit/clear button to return to the "blank home screen"→click the "STAT" button→click the "ENTER" button→*make sure all columns are empty*→input all x-values into the L1 column (press "ENTER" to go to the next row)→input all y-values into the L2 column→click the "GRAPH" button at the top right corner→click the "ZOOM" button→use the "▼' button to scroll down to the option that says '9:ZoomStat'→click the "ENTER" button→click the "2ND" button→click the "y=" button→click the "ENTER" button twice→click the "GRAPH" button→use the "▼" button to scroll down to the option that says '9:ZoomStat'→click the "ENTER" button→click the "STAT" button→use the "▶" button to scroll to 'CALC'→click the "ENTER" button→use the "▼" button to choose the option that says '5:QuadReg'→click the "ENTER" button→use the "▼" button to scroll down to the option that says 'Store RegEQ'→click the "VARS" button→use the "▶" button to scroll to 'Y-VARS'→click the "ENTER" button at 'FUNCTION'→click the "ENTER" button again→use the "▼" button to scroll down to the option that says 'Calculate'→click the "ENTER" button

Vertex (h,k)

☆Always the maximum or minimum ☆Can be found when in general form by 'x=-b/2a' and then substituting your answer in place of X to find Y.

DO THIS BEFORE STARTING ANYTHING (or else the calculator won't give you an r²)

☆Calculator Steps (click ENTER to select an option on screen): MODE→STAT DIAGNOSTICS→ON

Correlation Coefficient (r²)

☆Measures how well an equation fits a set of data. The closer r² is to 1, the stronger the correlation. ☆Calculator Steps: Catalog→DiagON

Axis of Symmetry

☆The axis is a line (x=h) which divides the parabola equally in half.

Maximum

☆The highest point on the graph when "A" is negative. ☆Only possible if the parabola faces down.

Minimum

☆The lowest point on the graph when "A" is positive. ☆Only possible if the parabola is facing up.

Zeros of the Function

☆The point(s) on a function where y=0. ☆The x-intercepts of the function. ☆Also called roots.

Y-Intercept

☆Where the function crosses the y-axis. ☆Can be found by substituting 0 in place of "X" and solving for "Y". ☆When the equation is in general form, the y-intercept will always be "C."

Standard Form of a square/quadratic function: f(x)= ax²+bx+c, where a≠0

☆ax²←quadratic term ☆bx←linear term ☆c←constant/y-intercept

Vertex Form of a square/quadratic function: f(x)=a(x-h)²+k

☆h←domain/x-value of the vertex ☆k←range/y-value of the vertex ☆(h,k)←vertex

Factored Form of a square/quadratic function: f(x)=a(x-r₁)(x-r₂)

☆r₁ & r₂←roots/zeros/x-intercepts

How to calculate the minimum

☆*click the "y=" button*→*make sure any previous equations are cleared* (unless you want to keep the information)→*type in the provided equation in the "/Y₁"= row* (don't forget the negative sign at the beginning or else the parabola will open upwards)(the variable button is the one next to the green "ALPHA" button)(make sure the "Plot1" button isn't clicked)→*click the "GRAPH" button in the top right corner*→*click the "WINDOW" button*→adjust the minimum x-value to 0 and the maximum to a number that makes it easier to view your parabola→click the "GRAPH" button→click the "2ND" button→click the "TRACE" button→scroll down to the option that says minimum and complete the same process as the maximum but for the minimum

How to identify the zeros of a parabola

☆*click the "y=" button*→*make sure any previous equations are cleared* (unless you want to keep the information)→*type in the provided equation in the "/Y₁"= row* (don't forget the negative sign at the beginning or else the parabola will open upwards)(the variable button is the one next to the green "ALPHA" button)(make sure the "Plot1" button isn't clicked)→*click the "GRAPH" button in the top right corner*→*click the "WINDOW" button*→adjust the minimum x-value to 0 and the maximum to a number that makes it easier to view your parabola→click the "GRAPH" button→click the "2ND" button→click the "TRACE" button→scroll down to the option that says zeros and complete the same process as the maximum but for the zeros ☆

How to find the maximum of a parabola

☆*click the "y=" button*→*make sure any previous equations are cleared*→*type in the provided equation in the "/Y₁"= row* (don't forget the negative sign at the beginning or else the parabola will open upwards)(the variable button is the one next to the green "ALPHA" button)(make sure the "Plot1" button isn't clicked)→*click the "GRAPH" button in the top right corner*→*click the "WINDOW" button*→adjust the minimum x-value to 0 and the maximum to a number that makes it easier to view your parabola→click the "GRAPH" button→click the "2ND" button→click the "TRACE" button→scroll down to the option that says '4:maximum'→use the "◀" button to slide the cursor left of the maximum/vertex→use the "▶" button to slide the cursor right of the maximum/vertex→use the "◀" or "▶" button to estimate the location of the maximum/vertex ☆The resulting x-value is the location of the maximum or minimum ☆Y-value is the actual maximum or minimum in relation to the equation